Yes. You can have a Claude account (free, Pro, Max, Team, or Enterprise) and a Console account (to access the Claude API) with the same email address. These two accounts will operate independently.
Claude Max and Team plans include monthly credits for the Claude API. To claim your credits, you link a Claude Console organization to your plan. Learn more about monthly API credits for Max and Team plans.
Tip: Sign in to the Claude Console with the same email you use for your Claude account.