My state is not yours.
In my state, if you are enrolled in a DUA approved re-training program and you got their approval before you enrolled in school (not necessarily before you applied for unemployment) you not only would not be denied, but you would be exempted from having to conduct a job search.
My state would also not object to your being enrolled in school if your classes did not interfere with your regular work shift. If you normally work 9-5 and you are taking classes between 7:30 and 9:30, they'd never blink an eye. As long as you're honest.
However, there are a lot of checks and balances that you do not necessarily see or know about, and if you lie to them, when they find out (notice I did not say IF they find out - I said WHEN they find out) then yeah, bad things would happen.

