What's the size?
(You should be able to keep the transformer/driver in the cabinet)
What color is the acrylic and how deep is it?
(If it's translucent white and at least 3 inches deep, you might want to add the LED's to the back of the sign, depending on the size, attaching the LED's to the side may create a dead spot in the middle.
If you are hardwiring or plugging into a wall in your state, it must be UL.
You can always ask...
Per a clients request, I designed lit ADA door signs and submitted them for inspection - my client was not UL certified but they had a sub-contractor who was, once we satisfied their requirements they passed it.