Even if you puke it up 15 minutes after you ate it, you still get some nutrition from it. Furthermore, puking and pushing are virtually the same. Sometimes, with a mom who is holding back mentally or physically, or is having a hard time getting into the groove of pushing, a good puking session can be the best thing that happens to her--you can't help but push while you are puking, and sometimes that gets the baby down a little more, and gives mom a feel for how it is all supposed to, well, feel.
I work at a birth center, and we encourage our mom to eat and drink whatever the heck they want. There are a couple of mexican restaurants right across the street--one birth a a couple of months ago, at 8 centimeters, mom was so hungry, she sent dad out for tamales. She ate two, lounged in the tub for an hour (and I mean lounged. I have never seen a mom so happy and beautiful during labor. She practically sang with every contraction, and was smiling and laughing between contractions until she began to push!), then pushed for an hour and had the baby. Ate the other two tamales about half an hour after the babe was born.
If it comes up, it comes up. So what? There are worse things in life. If you are worried about it, don't eat anything that takes a while to absorb, or that would gross you out if you puked it back up. Blended soups, yogurt, smoothies, anything that is already mechanically digested (meaning that you don't have to chew it, it is already blended in a blender or a food processor) are probably the easiest on the stomach.
They cannot do a damn thing about it if you bring food and eat. With your mouth full and a smile on your face, tell them "Well, you can just document that I am noncomplient and HUNGRY!" They also cannot search your bags and take things without a warrent. I know this for a fact because I had a patient one time that I was certain was injecting illicit drugs into her IV port. I saw her hastily put a syringe in a bag right when I walked into her room. Later, she asked me to get something for her out of one of her bags. I opened one, and she freaked "NO NOT THAT ONE! THE OTHER ONE!" but not before I saw the syringe...not a type that we use at our hospital. I went to my nurse manager and told her I wanted to search her room (I was scared--what if she injected something, then I gave her her valium as ordered by doc, and she died? Would I be liable, since I had good reason to suspect she was shooting up? Was I not protecting her? But if I withheld medications, what was my liability then?). The manager said absolutely not. It would be an illegal search and siezure, and I would probably lose my license over it if she sued. Just document everything and tell the doc (who did nothing).
So fill your bags with whatever you want! Eat, drink, be merry, and have a baby! Or better yet, birth at a birth center or at home, where you won't have to worry about it!!
... not my favorite moment, but once it was out I was fine... 
This pregnancy I am determined to shop a couple weeks before my due date... I want my sampler tray!!! 
