Yes, it can be done, but it is a very dangerous and complex circuit that many people with decades of experience (including me) would never attempt to make.
If you want a real sine wave output, you are looking at an enormous linear power amplifier, not something that can be built with thyristors.
Of course it would never give you the ISOLATION of a true transformer. But then many variacs don't provide isolation either because they are simply auto-transformers.