I don't think so..
G/L asks the O/S if any Window exists with a Title of either:

Print Ledger Financial Reporter
or
Maintain Ledger Financial Reports

In my opinion the O/S would be looking only in the memory space of the attached USER.

Note that this does not distinguish if the USER has the Financial Reporter in SAM and is trying to post in DAT, it will still be blocked.

Thanks Michael, I was also curious about if it was system-wide or restricted within a dataset so thanks for preemptively answering that question too!