If so, did they choose to go or refuse and stay?
At least in the WW2 they were. In Finland there was a battalion called Musta nuoli(black arrow) that consisted mainly of criminals and political prisoners. It was led by Nikke Pärmi, a convicted criminal himself. Much to everyones surprise, although I can't tell you why, many of them surrendered and jumped to Soviet side at the first opportunity, although later on they performed so well in combat that even finnish marshal Mannerheim personally congratulated Pärmi for their efforts. Source: Sari Näre & Jenni Kirves: Ruma sota(don't know if it's translated but the title means Ugly war)