I assume I will simply encounter some lag issues. PL was a bit laggy sometimes while I played it.
I'm still working through the DLC, since it's all new to me (ha ha). As far as I know, the quests of BS are activated after you finish the plain ol' main quest. The other DLC doesn't affect anything that happens in the rest of the game (with the exception of the added monsters, etc.).
I don't have the GOTY, so I don't know if this was fixed in the GOTY. If you have PL loaded, and are in the middle of the steel ingot hunt, there are about 12 ingots that you cannot access, because you fall through an invisible hole in the floor. There is no way around this hole. Trust me. So after consultation with Beth Tech Support, they told me to delete the PL DLC, and the hole would be covered up. And thus, it was. Immediately after I covered that section of the steelyard, and got all the ingots, I reloaded PL.
Note: this PL issue only affects that one hole in the floor, so if you don't care about ingots, don't bother. If you do care, I'd delete then reload. This is why I've always done the Pitt before PL, but as I said, I don't know if this was fixed in the GOTY.