search for objects that belong to an NACL

Yes, you can add permission-based search conditions via the Additional Conditions dialog in M-Files Desktop.

Note the remark on the user guide: "When you use the condition Access control list and select a named access control list that uses pseudo-users through metadata, it can be that the search results are not accurate or that there are no results." So depending on your NACL details you may or may not get accurate search results this way.