Nope, their budget is pretty much set regardless of who's buying them as they're restricted by FFP and proper reliable journos have said as such irrespective of if it's the Qataris or Ineos who buys them. FYI the figure I've heard for Utd is 100m + anything they can raise via sales, tbh it's not great but they had significant outlay last summer.
Woolwich have 200/250m+ sales as reported by David Ornstein among others, Liverpool have quite a bit of money saved up despite no CL, not sure what Chelsea plan to do (given how much they've already spent) Man City will be able to buy however much they want and Newcastle will probably be really comfortable with what they will be able to spend also.
That brings us back to us who I think will comfortably the least amount of money to spend out of all the top 8 clubs given how we've got large sums of money we still need to pay out for players.