It's hard to imagine Canadian courts finding such a law to be constitutionally valid, especially when it comes to using public services.

They've already dealt with a case involving a niqab-wearing woman  using a public service - testifying in court.  The Supreme Court of Canada found there were certain circumstances where the accused's right to a fair trial meant the witness should be unveiled, but went on to add:

"However, never permitting a witness to testify wearing a niqab would not comport with the fundamental premise underlying the Charter  that rights should be limited only to the extent that the limits are shown to be justifiable.  The need to accommodate and balance sincerely held religious beliefs against other interests is deeply entrenched in Canadian law."

~ R v N.S [2012, SCC} at:
 https://scc-csc.lexum.com/scc-csc/scc-csc/en/item/12779/index.do?r=AAAAAQAFbmlxYWIB