Taste wise I wouldn't use sweetened milk of any kind in a recipe in the place of unsweetened milk.

I don't know if it would set or not.

I made jello instant pudding today with oat milk. It has not set after 2 1/2 hours.

No

It will work if you put much less milk in it. Instead of two cups, stick with one to start with, then add a bit more. Go for a cooked version. That works better.
Cashew milk is tasteless so that is better, as is almost milk. Soy and oat suck as they are soy and oat-tasting.
Know that it will be much sweeter as you are using less liquid.

Will Almond milk work with instant no sugar pudding?