Nope, at 7 weeks, those were not acceptable/approved activities for our son's MLB directed rehab program or from Dr Andrews office protocols.
The mental side is tough, for sure, as has been posted before.
Swinging a bat could, to my thinking, create significant risk of damaging/tearing the healing tissue and/or especially damaging the anchor. Swinging a bat might help him mentally but I expect it would be short term because of the risks it creates in setting back the recovery/rehab. Same with taking ground balls, even though not throwing.
Your son still has to regain range of motion in the shoulder so that it gets very close to 100% in all measurements. I doubt any solid rehab program would permit him to incur the motion he would through swinging a bat before his PT shows a near normal ROM.
Just as important as his ROM, he needs to generate strength in the shoulder in each plane of his range of motion.
jsingerjj, this is a very tough, long and tedious process. There just are no quick fixes. There are too many variables.
I would encourage you to support and maximize your son's recovery by looking at this over the long term rather than possibly causing something negative to happen by what you might be seeing in the short term.
There are no short cuts as tough as that is to accept.