You can install Tor Browser for Android to a “Work“ profile on Android, yes.
FWIW, Tor Browser for Android only requires basic permissions required to function and doesn’t prompt the user for excessive permissions. Any of the tracking code carried over from Firefox for Android (Tor Browser is based on Firefox) is disabled in Tor Browser for Android.
So I am not sure if there are any added benefits for running the Tor Browser app in a separate Android profile.
Just a note there that using Tor Browser for Android, only the traffic from the browser itself will be going through the Tor network. Any other applications installed on your device will not go through Tor. For such a use case you might want to use Orbot.