Generating any new account comes down to generating a new Private key.
Once generated, it can be used on multiple networks (Because the Private key is nothing more than a random collection of 256 bits), and most blockchain networks work with 256bit private keys. Actually, I don't know of ANY large public network that isn't using 256bit Private key and 160Bit Public address.
So any new account you generated using Browne will work on any network. And you will be able to use it on the Avalanche network and deposit Avax there.
HOWEVER: DON'T use accounts brownie generated itself for testing/development, (the ones you might have used for development) because those Private keys are public and everyone knows them !!!!
If anything I wrote is unclear to you, or it feels like something is missing. Please ask away before deciding to use keys/addresses generated in brownie