You CANNOT vote with your tokens if you withdraw to a Coinbase.com exchange. You will need to withdraw to a Coinbase Wallet in order to vote and participate in governance. You can view all of the compatible wallets here.
Coinbase.com is a cryptocurrency brokerage where you can store your tokens after purchasing them. You can have a Coinbase Wallet without having a Coinbase.com account.
Coinbase Wallet stores the private keys directly on your device and not within a centralized exchange like Coinbase.com. Your Coinbase Wallet acts as a cash wallet and gives you direct and complete control over your own crypto assets.