Am I Able to Drink Anything and Eat Soft Foods While Wearing Invisalign?

The biggest issue is the trays trapping acidic fluids and giving the teeth an acid bath for hours and hours.  Normally teeth will get exposed to the acids during the meal, but then the saliva can flush and buffer the acids and neutralize everything to prevent decay (which is why they say chew sugarless gum, it's for the stimulation of the salivary fluids).

You are likely to cause cavities or even crack the trays.

Invisalign does not recommend eating or drinking anything besides water while wearing the aligners for  a number of reasons:
- you can break, distort, or damage the aligners
- the aligners can stain, discolor, or become dirty
- sugary foods and drinks trapped under or around the aligners can cause cavities
While it's probably safe to eat soft foods and drink other beverages besides water while wearing your aligners, I would avoid it. A better idea would be to remove the aligner, eat and drink what you were planning on eating/drinking and then replace the aligner as soon as possible. If you are able to brush your teeth and the aligners before putting them in, that is ideal. However, it can be difficult with a busy schedule to fit that in, so another acceptable option would be to rinse your mouth with water (or take a drink of water) before putting the aligner back in your mouth and then, when you are able to brush, do so.
Look, we don't expect you to starve while wearing the aligners, but obviously you want to limit how often you put aligners back in without brushing. The most important (and challenging) part of Invisalign is getting patients to be compliant and wear their aligners the required 22 hours per day. 

No, however if you find yourself in a situation that removing your trays isn't possible, be sure to rinse aligners and mouth as soon as possible.