I would suggest that it could be an extra unneccesary dynamic and could be misleading in a busy multi-crew operation
unless it forms part of your company's SOPs and you have been trained this way.
Best bet is to make it part of the departure/arrival briefing and get the PNF to call TA on reaching/passing. Some companies use MSA as the trigger to set standard when cleared to a FL on departure.
Whilst in the descent set QNH (maybe already have QNH set on the standby altimeter when you initially get ATIS?) and go into approach checks
when advised to descend to an altitude by ATC.