As a non-tournament player, I can't say that any non-loyalty race themed decks can or cannot compete competitely against decks designed to win tournaments, though I very much doubt it (but who knows what coming years will bring).
I can say, however, that in casual play (that is as compeititve as it can be, and featuring all expansions and ownership of 3x of every card by all players involved), the four races in question have respectalbe win ratios, some of them just as much as loyalty races.
I would not go so far as to say that these races exist only to augment loyalty races, although I would agree that is their primary use at this stage of the game. As noted, each of those four races have cards that are most useful in decks heavily featuring their own kind, examples being Pageant of Shrikes, Chittering Horde, and Blessed Spawning.
My Lizardmen and Skaven decks feature only cards with their racial trait, the single exception being Contested Village. Both of these decks compete well against both loyalty race decks and mixed decks, particularly the Lizardmen. Lizardmen, I feel, have the best direct-damage capabilities in the game right now after Chaos. It's not too difficult to get the Loq'tza machine gun engine going quickly with just Lizardmen cards by giving each "bullet" high damage output with several Lizardmen units in Loq'tza's zone, particularly with Terradon Riders, who will in turn also supply the resources necessary to fire multiple times if you're doing all this in your Kingdom. Blessed Spawning gives you some "ambush" and surprise capabiliities, particularly with Chakax out. And any unit in play with a single damage on it is just waiting for a death sentence from Spawn of Itzl.
Skaven has cards most effective with maximum Skaven cards in your deck, notably Chittering Horde, granting you 4 or usually 5 cards draws, at just about anytime in a game round you want, for a mere one loyalty-free resource. Both Skaven heroes are disgusting in a deck of near all Skaven cards. Skaven, despite most new Skaven cards working against this, are at their best when they are cheap and plentiful, unloading multiple threats a turn that, if dropped one at a time or in slow succession, aren't too difficult to eliminate or contain but all at once or in quick succession can be overwhelming. Particularly evil is getting Night Runners into your Kingdom early and playing Warpstone Experiments on them at the beginning of your next turn, giving you a large boost in resources (and therefore, units), then slapping your opponent with 4 or more (if you played some Clan Rats) indirect damage at the end of your turn before the Night Runner or forced to exit play. Of course, the longer the game goes on, the Skaven's chances of pulling out a victory diminish exponentially.
Undead are deathly effective even on their own, but I've never shed the DElf supplementation since the Undead first arrived in March of the Damned. Today I have about 4 different DElf cards in my Undead deck, most notably the Slave Pen due to it's great synergy with the Necromancy keyword. Also, the DElf units allow you to make use of cards like Drakenhof Castle if your opponent's discard pile has already been depleted of non-undead units by such cards. Aside from the two already mentioned support cards, I only run three other non-unit cards such as Hidden Crypts and Danse Macabre to maximize Vampire Bats and Necromancy. Unit elmination is strong with the Undead with cards like Wight Lord, Blood Dragon Knight, and Danse Macabre, only helped by the DElf cards, all of which do this without damage, aside from Blood Dragon Knight.
Wood Elves are, as stated, the most difficult to make use of. On their own, they were particularly weak due to heavy resource dependence and heavy development dependence, and if you're relying heavily on developements, you cannot rely on the cards in your deck as they will end up as developments off the top of your deck, and you will either abandon the developement strategies, or not beable to build your zones with cards that generate resources, draw you more cards (necessary for development strategies), or get attacking power necessary to win before you end up decking yourself. All this also makes you vulnerable to attack without much in the way attacker elimination.
During the Morrslieb Cycle, I tried to get the Wood Elves going with heavy reliance upon Dwarves, as both races share synergy with developments, and the Dwarves have good unit/attacker elimination with cards like Durigan and Slayers of Karak Kadrin. Ultimately, however, newer Wood Elf cards were not helping things along and it was simply becomind a Dwarf deck with wood elf liabilities involved. I dismantled the deck early in the Capital Cycle and decided to wait until the Wood Elves became good at something besides decking themselves.
With Portent of Doom, I decided it was time to see how the Wood Elves do going it alone (or at least with out loyal race cards). I tried out a build with the new Wood Elf quest, making units like Blade Dancer and Forest Dragon viable as units not to be played, but to come into play as developments that become ambush units when the quest goes off. Forest Dragon, Wild Rider, and Drycha become untis that can end the game thorugh combat before you deck yourself when you get your developments and resources going, helped out by cards like Dance to Loec, Armory, and the restricted Innovation. You also don't have to feel that developments rob you of cards key to your strategy, as with no non-Wood Elf units, Pageant of Shrikes lets you pull back developments into your hand to use as the actualy cards, while also robbing your opponnet of any developments that he is using as part of his strategy for cards like Troll and Serpent Slayers, Burn it Down, and the like. Not only are most Wood Elf supports of limited or questionable use, none of them are buildings, making the Treasure Vaults resource engine nigh-useless in a strictly Wood Elf deck. I currently use Contested Village and Armory, and would like to fit in Contested Stronghold. With those nine buildings, adding Treasure Vaults would be great for resource generation, with 12 total cards that can benefit from that.
With the increased use of Quests, I'm hoping we see a new boxed expansion soon that showcases more quests and brings Bretonnians into the fray in major way.