I have published my feelings on this topic elsewhere, but as long as Liverpool don't finish 4th I really couldn't care less who does (as long as we finish 3rd!). To be honest, and Im not trying to wum when I say this, but I don't think finishing 4th will be remotely constructive for Arsenal overall. Like last season, it will only serve to cover up the cracks that all but Wenger and your board are so blatantly aware of. In all honesty, I don't think 4th would be enough to hold onto RVP- which is a shame b/c he's a flipping class act and his loss (presumably to Barca or Real) would ultimately be the PL's loss.
Another season finishing 4th (perhaps with an FA Cup to show for it; with all due respect you are NOT good enough to win the CL!) would allow the clowns in charge of your club to merrily watch another transfer window stroll by w/o the MAJOR investments that Arsenal- quite frankly- are desperate for.
I can't see you finishing 3rd, simply b/c I feel Spurs are just too far ahead at this stage of the season and have already shown that we can cope quite well with mid-season distractions (whilst they may not be on the same magnitude as this, Harry missing a few weeks after his operation, the Olympic Stadium affair, and the recent tax trial all passed quite smoothly at THFC).
Whether or not Wenger stays, a 5th-place finish may- in the long run- do more good than harm for you, as it will galvanise long overdue action from your board and manager.