The Kitzur Shulchan Aruch states in סימן יא - הלכות מזוזה that a house where a non-Jew lives is exempt from a Mezuza.
בַּיִת וְכֵן חָצֵר שֶׁגַּם גּוֹי דָּר שָׁם, פָּטוּר
He also states (ibid) that if one affixed a Mezuza in a location that is exempt, and that location later becomes obligated, one has to remove and re-affix it.
מִשּׁוּם דְּבָעֵינָן תַּעֲשֶׂה וְלֹא מִן הֶעָשׂוּי
So if a soon-to-be-convert affixes Mezuzot, they will have to remember to take them down and re-affix them after the conversion.
(I didn't research this further, but it sounds like asking for trouble; this crucial step could easily be forgotten in the excitement, and then the Ger would be living without a kosher Mezuza.)
Reminder: Mi Yodea is not a replacement for asking a Rabbi.