On the contrary, I think that it makes a great deal of difference indeed with regard to the peace and security of the region because the Haram al-Sharif is a very major point of contention in the conflict between Jews and Palestinians.
It seems to me that for Jews to continue believing that the Haram al-Sharif is the site of the Temple Mount, then the archeological evidence uncovered so far needs to support this view.
However, the fact of the matter is that after 40 years of the most extensive archeological excavations at the site by Israeli scientists using the most modern and sophisticated intruments available, all of these excavations have failed to turn up any tangible evidence whatsoever that there was ever an ancient Jewish temple there.
Therefore, the logical and sensible thing for the Jews to do now is to finally acknowledge that the Haram al-Sharif is simply not the site of the Temple Mount and for them to continue their search for the location of the lost Temples elsewhere.