Back when I was still doing mammoth sessions with my main group we used to routinely do snacks and meals without seriously impacting the game. The fact that the players are sitting there munching on Doritos and Dominos (the other D&D :P) was no more relevant to the game than the fact that we were rolling dice instead of actually swinging swords, or that the Barbarian's player just had to go to the toilet in a hurry.
Immersion is great and all, but there's only so far you can take it before you stop roleplaying and start play acting.
As for the mechanics of how you go about fitting the meal in, there are lots of ways that you can free up a player or two if someone needs to go make a food run. A lot of our sessions included points where one or more of the characters were involved in an event that didn't include the rest of the party, which is an ideal moment to duck out to call the pizza place or even hit the drive-through if the episode is a long one. You might miss a few details that your character wasn't privy to anyway, just clear it with the GM and the group before you take off.
Another option, if getting away from the gaming table is required, is to plan a section of the game that doesn't need props and such. We spend a lot of time just talking, might as well do that at the dinner table as anywhere else. How well this works is going to depend on the group and the nature of the adventure of course. Not every game situation lends itself to a half hour of sitting around just yakking, and you should always keep a few dice handy for some ad-hoc decision making, but if you plan a low-key interaction over that time and make sure the players don't decide to launch a new combat with the enemy army over the hill, you might be OK.
Or, if all else fails, night time when everyone (except the poor sucker on watch) is asleep is probably a good time to pause and take time out for a meal. Then you can surprise them with a midnight encounter when you're all feeling nicely sleepy from that impending food coma.
From experience though, I have one suggestion to make: make sure you have plenty of paper towels or similar around so that nobody touches a character sheet, prop or die with hands covered in pizza grease or chip crumbs. Bad enough that we can't keep these things safe from the occasional beverage incident, don't let food on them as well :P