If a meteor hit Rome, left a crater, but did not cause any massive damage (unlike a truck-sized one which could get rather hairy) the people on the street would very likely consider it a sign of divine wrath. They would more likely tie it to the war in Germany, or the French revolt, or the troubles the Stuart dynasty is in, or the latest conflict with the Turks, or just about anything at the to of the agenda rather than an old and rather obscure Inquisition case. After all, Galileo only becomes a cause celebre after the majority of people realise he's right.
The stone itself would have to be explained somehow. Perhaps a group of experts would use the opportunity to develop an idea of 'bits breaking off planets' or similarly mundane explanations in order to point out how stupid the Muslims are for venerating such a bit in Mecca. I'm fairly sure that prior to Newton, nobody would even try to come up with the idea of bodies 'floating' in empty space. I don't think the Curia (unlike the preaching orders) would accept a simple 'miracle to show the wrath of God' conclusion.
Interestingly, this could result in the Catholic church having a system that explains meteorites whereas the Newtonian-Galileians in the 18th century do not. Might some scientists become more pious?