Is it possible to use MODX snippets/tags in Twig templates?

Yes you can! The twig templates will be parsed first, but Commerce also processes the result through the standard MODX parser afterwards for even more flexibility. That means you can even use Twig templates to build MODX tags (but not the other way around).

Some of the snippets included in Commerce are also meant to be used with chunks, instead of twig templates.