I appreciate what LL is saying, and I don't think they are at fault for the entire pitch issue, but there can be no doubting it's a problem they've contributed to.
Under the terms of their agreement they are entitled to use BP, and I have no problem with that as such - but if they are only pulling in 1000 people a game (ish) then they really do not need somewhere the size of BP.
If in 5-10 years time the new arena is built and the pitch has been invested in - with under-soil heating, improved drains, improved covers etc etc then I'd welcome them back - knowing that they would have considerably less impact on the surface, and that they would be contributing to the 'community' aspect of the ground (giving them some space for an office, ticket sales desk, a section of the club shop etc.) and looking for possible integration of the clubs on some level.
But right now - from a cost/benefit analysis point of view - I think they are a hindrance not a help, so as a result I've voted no.