As far as I'm aware, none were ever authorized, but the Cross of St George was unofficially tolerated. Many cavaliers of the order wore their crosses underneath their Soviet medals. Nedorubov is a famous example, a Hero of the Soviet Union and Full Cavalier of the Order of St George. Even in official photographs, he's shown wearing his unauthorized crosses. Here's another photo of a higher ranking officer, Vasiliy Kniga. Even though he was awarded other Tsarist medals, the crosses are the only ones he has on in that photo.

There was a decree drafted in 1944 by the Council of People's Commissars to equate the crosses with the Order of Glory, officially allow them to add the ribbon of St George to the ribbon bar, and grant all benefits of the Order of Glory, but the decree was never implemented.

In Orlando Figes's A People's Tragedy, he writes:

"[The] symbolic revolution was also enacted on a personal level. People made a conscious effort to distance themselves from the old regime and to identify themselves with the new democracy. Soldiers renounced their hard-won tsarist medals, and often sent them to the Petrograd Soviet so that it could melt them down and put the silver to the use of the people's cause."

It seems like few people wanted their medals at all, though the feeling I get is that some peasants may have been more likely to want to keep medals, and Figes doesn't give us any data about the extent of this, so I can't say for sure.