Playing rhythm, it shouldn't make much difference, but lead or hybrid picking would be much more difficult to do. In hybrid picking you use the pick, and the middle, and ring finger on the right hand.

Playing lead riffs, you could use a flat pick only, but when it comes to rolls, and other speed techniques you may find it hard to do.

I know all about retraining, I was a flat picker for 17 years. I always used the flat pick only, and then took a road gig with a country band. I still use a flat pick, but had to train myself to use my fingers too. Most of what we were playing had double stops, and they just sound better played with the fingers.

Your situation may be different, and it's really up to you how you play. You have to do what makes you the most comfortable, so hold the pick any way you want. The music we play is a way to express what we feel, and if it sounds the way you want it to, then it's fine.

JD