Yes, you can usually deposit a check drawn on another bank into your account for clearing, provided the check meets the required conditions and regulations.
Key points
An initial entry on the account doesn't always mean the check has been cleared; it could still be returned as a bounced check.
Ask your bank about the clearing timeframe, fees, and availability date before considering it as a final balance.
The figures, fees and limits in this answer vary by bank and change over time — confirm them with your bank or the official source before acting.