Yes you could visit him in Kingston. They stopped running people from Manitoba out of the city a few years back IIRC ;D (just kidding!).
There is a very strong possibility that he will have a wait between his ATIS courses, and BMQ. Once he completes BMQ, he will likely be posted to Kingston at CFSCE (http://www.army.dnd.ca/asu_kingston/military/cfsce_e.asp) but Attached Posted to PRETC in CFB Borden to await his POET (Performance Oriented Electronics Training) and his ATIS QL3 (basic trades training) courses. For how long? He won't know that until later. There is a POET course starting approx every 2 weeks during the year. He will likely have a gap in time between his POET and QL3 as well. All in all, he can expect to be in Kingston between 12-18 months, roughly. The only way he can expect to avoid this is if he has some electronics training prior to entering, and received a POET bypass or something, in which case he will forego that training.
As for you visiting, yes by all means you can. There are decent 'rooms' on the Base for $35-$40 a night that are quite nice too, to help cut down on the expenses.