Can my tax preparer file my tax late without putting in a extension for being late

Why would you be late?   If you owe tax and will be late regardless of the reason you need an extension and pay any owed tax by the due date.    If you are getting  a refund then there is no penalty for being late - it just delays the refund.

Yes. Since you are asking about filing late, I assume you are talking about 2020 (or perhaps earlier). It's too late now to get an extension for 2020. You just file late, without an extension. Even if you had an extension for 2020, it has already expired. So you are just filing late, whether or not you had an extension. If you are getting a refund, there is no penalty for filing late.

If you are late, it's too late to request an extension of time to file.