Yes, at the time of applying and at stage 3. If you are at stage 4 green (no need to send other documents, analyzing), than theoretically you are fine.
There are some issue just now, specifically now. Since April 1, additional check with external authority UCFE is added, and there are reports that all processes on the stage 4 were returned to stage 3 for that additional check, and status does not show it.
Theoretically, you had a reply from AIMA already, and everything is good from that side, however it is not clear what happens if permit will expire while you process is waiting the reply from UCFE (IRN knows the date from AIMA reply). It is always a risk to let permit expire and not renew during the naturalization on residence.
There are also anecdotical evidences that when permit is expire soon and process is at stage 3, IRN might be not in hurry to pass through that stage. People say that it looked like IRN was waiting for their renewal and just after the process moved finally.