Yes your partner can come visit but you would have to pay their airfares as I believe there are no staff travel privileges until training is over, however this might have changed so I guess you can always ask.
As you may be sharing accommodation with another trainee then you may also have to factor in getting your partner somewhere to stay as you can't really expect them to bunk in with you and another trainee while you are trying to study. Having said that it does depend on the accommodation, as for some it has been single rooms in hotels and otehrs have had 2 sharing an 'apartment' style hotel room with separate rooms, kitchen etc.
Either way I would check with the company to see what the policy is and what is allowed- some hotels will want an extra fee for an extra guests and some may not allow visitors to stay overnight.
Do remember that you are at work the whole time of groundschool, it's not a holiday. Quite a few of us during my training had partners just come visit for the weekends or days when we had off.
I echo the sentiment tha recruitment are busy, the more you call them the more you distract them from processing applications.