In theory, yes.
However, it could be that some, or all SSD controllers require a polling signal to remain awake. No polling signal from SATA, then the controller itself may enter sleep mode.
I'm only saying this could be the case, as no manufacturers have stated IF an SSD controller requires polling to stay active or not, and I'm not aware of any study that has examined an SSD only powered, but not SATA connected will do GC.