Can Brave Rewards earnings link to the Brave Wallet?
No, it will not happen, or it might be difficult because BAT is an ERC-20 token which results in paying a lot of gas fees for a small amount of BAT rewards transactions.
In Gemini and Uphold, there is an internal transfer of BAT payout to users, which results in zero fees.
Obviously, you will not end up paying $20 fees for 5BAT token deposits.
Anyway, this is my point of view.