I say yes, you can. In my practice, using human cells, I perform the lysis and I freeze all samples at -80°C. In this step, freezing helps to disrupt cell structures. I thaw the samples, perform the purification and I aliquot the samples and again freeze it again at -80°C. After these two steps of freezing, I avoid any freeze/thaw cycle. Like that my samples have an homogeneous number of freeze/thaw.

Thanks Stéphane! In my lab no one did that before, so I had some doubts about it.