No, Rempe cannot be a decent 4th liner in the NHL. Yes he moves pretty well for how freakin' huge he is, but it ain't like he's Chara.
On top of that he only has marginally better hands than Kurtis MacDermid. And if MacDermid fought other players as much as he fights the puck, he'd have broken the PIM/fighting majors record about twice over by now.
Also, his mind simply doesn't move fast enough to keep up with the play, and it's only gonna get worse as time goes on. Nope, as Henchy says, he's in the NHL for one reason and one reason only. There is no hope for him to be a poor-man's Tom Wilson, or even a young Ryan Reaves (who BTW in his prime probably looked a lot better than he did because Hitchcock sheltered the living bejeeezus out of him, wouldn't even let his line take faceoffs).