No. Rashi was a tremendously great scholar and recipient of oral traditions from the schools of Germany, but he did not receive supernatural ruachruah hakodesh.
The Ohr HachaimHahaim (who lived a few centuries after Rashi) writes in his commentary to Genesis (6: 3) that after the destruction of the Temple prophecy ceased but Ruach Hakodesh continued. (I presume this refers to Chazal; the sages of the Talmud). Afterwards, however, there is no ruachruah hakodesh, and there is not even traces of "reiachreiah hakodesh".
"Afterwards" seems to refer to the post-Talmudic era. (References to "these days" to refer to the post-Talmudic era are common in rabbinic literature).:
ומשחרב המעון נסתם חזון ונשארה בחינת רוח הקודש, וכשנסתתמו עיני ישראל אין אתנו משיג ריח הקודש ואין צריך לומר רוח הקודש
A more limited form of his statement can be found in the Tosefta Sota (13:3), Bavli Sotah (48b) and Sanhedrin (11a) which states that after Haggai Zekharia and Malakhi died, ruah hakodesh was removed from Israel.
Note also the following passage penned by R. Dr. Haym Soloveitchik :
Most people...have heard in their childhood-the story goes back to the fourteenth-century Spain-that Rashi's commentary was written be-ruah hakodesh (inspired by the Holy Spirit.) Plausibly enough, for how else could he have known all of the minute details of the countless Talmudic narratives, not to speak of is command of the underlying concepts of all the talmudic discussion...? I here suggest that these astonishing feats can be explained without recourse to miracles-a proposal, if you wish, by a litavk to counter claims of ththe Holy Spirit. [2]
He proceeds to frame Rashi's knowledge as stemming from tradition.
[2] The 'Third Yeshiva of Bavel'. Published in Collected Writings II page 151.