Oh great. Now I’m imaging White Diamond using tape to stick Pink’s fake gem shards back together.

Serious answer; It’s plausible, but I imagine that if it did work, then the gem wouldn’t be in tip-top condition. They’d probably look slightly deformed and act a bit loopy.

I suppose Steven would be able to heal them - assuming you could find all the pieces of a discrete gem.  I guess the problem would be that when gem's shatter, they seem to do so much like glass (based on the fragments Pink created to simulate her own shattering).  Little bits would go everywhere, some really small.  Given most were shattered in battle, I don't suppose one could actually gather them all.  Much less match them to a specific gem.