Yes you can - usually I think it's advisable to wrap postgres in a shim application to provide a consistently defined surface you can control but postgres can absolutely serve as the authority node on data correctness.

As to which technical solution would be optimal there are a bunch of factors to consider and I think preferences around features could lead you to a variety of options. Postgres is excellent as long as you're minimizing the amount of data piping directly through it or operating at a reasonable scale.