I have Invisalign, you can, but it sucks. Kinda feels like eating something that is in a plastic bag that has a little hole in it where you can still taste it.

I thought about the possibility of DIY Invisalign. My ortho basically did this once and gave me trays that he made in-office.

Obligatory: "orthodontists hate him"

No you take them off to eat.

http://www.invisalign.com/how-invisalign-works/living-with-i...

Food finds its way up between the aligner and the teeth, and it's very unpleasant. Not recommended.

Drinking is not a problem though.

Most orthodontists will say anything except water is a no-no - coffee and tea will stain your aligners, and they almost always permeate the aligners into your teeth, causing decay until the next brushing. Juice is even more harmful with the sugar and fibre. Also, hot beverages can deform the aligners. I know cases of people who tried having drinks with straws, and realized it wasn't a viable solution. The drink still ends up permeating the aligners.