I think I would have benefited from upskilling before graduating, so I'll go against the grain and say it might not be a bad idea.

I graduated in 2012 and had to spend a year after graduating upskilling, because my program left me woefully unprepared for the job listings available, and my GPA wasn't very good, so I wasn't qualified for any internships while I was studying.

My situation might have been a bit different though; I spent 9 years getting my bachelors part-time while working full-time in the service industry. I never learned more than the bare minimum to pass my classes and didn't realize how important it was to do that while in university. I also never really absorbed the knowledge learned; because I wasn't applying it while learning it was all very abstract to me.

After graduating, I realized every entry level job expected a bunch of knowledge I was lacking, so I spent a year doing online MOOC courses and working on personal projects. Then after a year, I met someone at a conference who gave me part-time paid work that we called an internship (I was very marginally productive during that time, as I was still playing catch up, but I wasn't making much so I think it worked out OK for both of us)

Taking time to apply the knowledge and build personal projects before graduating would have been a boon to me, as a lot of opportunities for things like internships were no longer available after graduating. I think the whole situation set my career back by 2 or 3 years.

Also, considering this is one of the worst economies to graduate into, you need to be able to hit the ground running once you graduate, with as much experience as possible.