I'd be rather interested in the DW-based Inquisitor build. I, for one have noted that, on the few occasions where I have had ladies playing in my games, the three of them got as uncomfortable playing males as I do playing females. With Sisters of Battle being a bit to out there/fanatical, an Inquisitor, or one of that individual's higher-end Throne Agents would make for a nice alternative, if it proved necessary to not alienate players, especially if it balanced them out, so that Space Marines don't feel overshadowed. I don't dislike Influence, but prefer Profit Factor called Influence, and would hate to see so connected a person limited to the same Requisition system Space Marines are relegated to.
I do kind of wonder though, other than getting ready for a mission, how much social endeavor goes into a Kill Team's job, that the skill monkey Inquisitor can make them feel worthless? Imperials look at Space Marines like gods, the Inquisitor won't be too social with other Space Marines, not knowing all of their fluff, and the enemies aren't often talked to; those aren't the kind of enemies Space Marines are thrown at. Is it a particular list of skills that Inquisitors can outshine them, like better Tech-Use then the Techmarine? I figure usually Space Marines fight, and they'll stay better at that, then Inquisitors, minus gear access.
To be balanced in DW, an Inquisitor absolutely must be subject to the Requisition rules.
Both Ascension and Rogue Trader take a very cavalier attitude towards equipment. If you want something, you can have it in two sessions tops. Which is (mostly) fine for those games, as stacking up on equipment can only get you so far, and because both the big =][= and Rogue Traders are known for their bling. Also, each and every character has roughly equal access to all the cool stuff, which moderates the internal balance of the party
In DW, equipment is a f***ing big deal, both because Space Marines are unreasonably deadly even with just their combat knives, and because while Astartes are renowned for their superb gear, they aren't exactly known for piling it on particular Battle Brothers. Hence, you get your standard loadout, and whatever you want to better fulfill the specific mission. If you want more equipment, you have to pay for it in exp - that's something completely unheard of in other 40k games, unless you count certain Tech-Priest talents as masqueraded gear (not an entirely baseless assumption, considering many TP toys got rewritten into equipment in Black Crusade, but marginal enough to not impact my point). Basically, the worth of every equipment upgrade is much higher in DW than it is in other 40k games.
Now, if you want an Inquisitor in DW to have the same access to gear he'd enjoy in an Ascension game, you have to make a very important choice. Either you let him requisition superior equipment only for himself, or you allow his unquestionable authority to override the limitations on Astartes players as well. If you choose the former, you create a potential balance concern when the Inquisitor is stacked through the roof with best craftsmanship equipment for every possible contingency. This isn't likely to be a serious balance issue, considering how buff the Astartes are even with their basic gear, but it does seriously undermine the idea that Deathwatch characters are superbly equipped, and thus may drop the willing suspension of belief or just plain destroy the fun of Astartes players.
If you choose the latter, well, you just seriously broke any semblance of balance DW may have had. Forget about the careful selection of best gear for the mission, the Inquisitor has an open tab, so everyone gets relic plasma guns! The mission is too low-key for Battle Brothers to be trusted with holy Terminator armor? Not when the Inquisition is paying the bills - fighting the Orks has never been easier! And since the Inquisitor is requisitioning our gear, we can pool all our Requisition for demanding assets as the mission demands! Yay, orbital strikes and friendly Vindicare snipers providing fire cover.
The solution is to force the Inquisitor to abide by the same rules as Marines, but giving him slightly more Requisition or more Signature Wargear so he can pimp himself out properly without being able to use anything and everything described in the books on a whim. The unquestionable authority of the Inquisition would also need to be represented differently, in a way that helps overcome obstacles but doesn't obviate them automatically.
As for the other point you raise, much depends on the particular group, but Deathwatch has the potential to be intensely social. Combat is the most obvious focus of the system, but it's also the hardest for producing strong emotional reactions. Marines often take combat extremely casually, and often so do players, confident in the knowledge that their characters are way scarier than eighty percent of things they can encounter in the course of the mission. The most interesting DW scenarios are those focusing on objectives other than simple martial victory, and social interactions can play a crucial role in creating tension. An IG commissar will treat the Astartes with reverence and deference, but he's not automatically likely to change the orders handed down by his superiors to incorporate the Kill-Team's plans. Allowing an Inquisitor to use and abuse his Influence on all the NPCs around may cheapen a lot of potential stories.