The short answer is yes, you just cut the foam section out around the hole, fill the hole like normal and then reapply the foam with suitable glue, more details can be found on:
ContiSilent Repair Guide (works on Michelin as well)
What do the insides of the tyres look like?
Basically, they’re just normal tyres with a thin strip of sound deadening isolation foam inside, nothing special and not unique to Tesla (although this video seems to indicate that is the case).