Any top manager would get that Liverpool side to challenge for 4th spot. They will not look magical in their wins, but they sure as hell can eke the points out week in and week out once they have a proper system and sane management in place. Plus, top managers will attract top players, especially given their stature in English football.
That said, I'd rather they went for Ancelotti than Klopp. The former will give them good runs in Europa League/CL and cups, but not be very effective in the league.
Shouldn't be a problem for us specifically per se - Arsenal and Chelsea are equally vulnerable to losing the CL spot right now, and the only way is up for us, given the potential in our squad.