We don't know. That is the traditional religious interpretation of Sura al-Fil but other than the Quran itself and the tafsir, the latter of which in particular is historically suspect while the former is, as you can read from the verse in question, both vague and mystical. If Abraha did attack Mecca in circa 570 we can be reasonably certain that he was not defeated by a miraculous flock of birds, however.

Abraha himself is better attested to in the sources as the conqueror of the Himyarite Kingdom of Yemen which had until that point been dominant in southern Arabia, so it's not implausible that he would march north, we just don't have any sources to that effect. Our sources for his presence in Yemen, on the other hand, I understand are quite good including mentions by Procopius and an inscription on Marib Dam. edit: He is known to have launched an expedition into central Arabia (and another by his allies) which are equated with the content of Sura al-Fil but without additional sources there is no way to verify this.

Pre-Islamic Arabia, with the partial exception of Yemen, is in general source-poor, and there are even revisionist historians who doubt the existence/location of Mecca itself due to this lack of sources. That's a bit radical for most historians (and myself!) but the general consensus that I've come across is that Mecca was probably less prominent than the tafsir and other Muslim sources would suggest.

edit: Source-wise, see Robert Hoyland's Arabia and the Arabs: From the Bronze Age to the Coming of Islam.