Maybe. It's hard to say. IIRC, Jerusalem being the site of Mohammed's ascension is not based in any Islamic scripture except vaguely and was interpreted that way a few hundred years later. The tie to the Temple Mount location is even more tenuous. It was my understanding that the DotR falling into disrepair was because of simple neglect -- Muslims don't actually do much worshipping there, it seems to be more of a show of dominance -- but digging would explain a lot.
I do remember on a previous thread that the Holy of Holies explanation was pretty emphatic by those who knew.
Needless to say, this wouldn't be much of a reason for dismantling the DotR or even for building a new temple.
I remember reading that Muhammed actually never went to Jerusalem and have heard the same also.