Setting the FAF altitude on the FCU with altitude constraints on the way will work in principle when:
- flying a full procedure that comes with stepdown altitudes correctly coded in the database,
- flying in DES, not any selected mode.
However, bear in mind that ATC only sees Your FCU altitude and does not know whether or not You are going to keep the higher altitude constraints. There are airports where there is a major separation issue behind those: consider LLBGs RNAV Visual GAVRI 30 or the RNP X where You are to maintain 5000´until REBDO to keep clear of possible go arounds that will climb 4000´and cross below You and also 26 departures.
So I would strongly advise using either selected descent or, at the very least, keeping the FCU altitude synchronised with the currently cleared altitude. In LLBG, this is even a requirement.