I got into CoC only because I found the old CCG-era booster boxes online at fire-sale prices. At the time I just wasn't ready to commit hundreds of dollars to yet another card game, so buying several thousand black-border cards on the cheap was a great way to test the waters. The CCG has some neat cards in it that really help when designing theme decks (my favorite kind), so I'm glad I did.
Up until recently (when I decided to set up a regional tournament), most of my decks were a mix of black- and white-border cards, and they were a ton of fun to play. I know the general consensus is that the CCG-era cards are unbalanced and too powerful when compared with the LCG, so you shouldn't mix the two. I don't agree. In fact, I find the LCG cards are actually better overall - better cost, better abilities, better combos. We've battled all black-border and all-white border decks, and the black-border decks almost always lose.
It's true that the CCG had a ton of cost reducers that can make cards stupid cheap to play, but other than that, in my experience there's not much in the CCG that the LCG can't do, and do it better.
Also, one of the only ways to get the cool domain cards is to buy the old Arkham and Eldritch edition starter sets. That alone is a good reason to invest in at least some black-border cards.
There are two primary reasons for not buying/playing with black-border cards:
1) As dboeren said, if you like to discuss your deck strategies online, then stick with the LCG. Otherwise, you're really playing a different game than everyone else, and that can make it hard to solicit and offer advice on this forum.
2) If you want to play in tournaments (though there aren't many), then put your money toward the LCG.
However, if you're playing in a friendly environment and can find the black-border cards for cheap, I don't see why not. I bought a lot of them and don't regret it for a second.