Do Disconnected Remote Desktop Sessions Lock Accounts?

I have not encountered any scenario where an account is listed as unlocked and the user is getting account locked issues. However, this could potentially occur if the DCs are not up to date.

Are the users who are getting this problem all within one AD site? Generally your intrasite DC replication will occur fast enough to avoid these issues. If your intersite replication schedule is too long and a user somehow gets locked in a separate AD site you could have the scenario you encounter.

Have you tried looking for the root cause of the account lockouts? You could use the Lockout Tool to find where the bad logon attempts are coming from.

If the setting is unavailable on the properties of the RDP protocol then it's being set via Group Policy. You'll need to check the GPO's that apply to the server in question and configure the setting there.