My research, and experience, says no.
A bit of a head scratcher for me, especially with the NCAA's much ballyhooed latest ruling that allows $0 players "to transfer without having to sit out a year." No one ever mentions that to benefit from this "no penalty" transfer opportunity, is it must be done in the summer. Between seasons.
Once a player sets foot in the classroom for their fall semester, $$ or $0, they now are subject to the "365-Day Rule," which says (my interpretation): if a player leaves a team during the school year they may not play for another team until 365-days has elapsed since their departure from original team. $$ or $0.
Now, one can appeal to NCAA I'd imagine for extenuating circumstances, but no guarantees there.