No you can't.
The whole point of the SafeZone is that it is isolated from your normal system, it uses a custom browser, currently based on Chromium (not Chrome).
This SafeZone browser may possibly change in the future, but the concept will be the same a custom browser within the SafeZone (with everything isolated from your system).
EDIT: That said I don't know if you could use Edge sandboxed (in the avast SandBox function), which is somewhat different to the SafeZone. Of course since Edge is very new and only in win10, I don't know if that option would be compatible.