Having worked in a couple of diners, and other assorted restaurants, most take a large delivery about once a week. That's not saying that they would be completely depleted in a week, but rather that the most commonly sold items usually last about that long.
But we're specifically talking about a diner here so lets take a look at that.
In an average diner, sadly but not surprisingly, most items aren't what you would call "fresh". Apart from a few staple items like:
- onion (sometimes pre-washed and cut, sometimes frozen, on occasion fresh and whole)
- and some sort of pre-washed, cut salad mix
Nearly everything else will be frozen, dry, or canned.
All of your meats and most of your veggies, will probably be IQF (individually quick frozen)
Don't expect to find much in the way of unmixed dry ingredients like flour. Most pancakes, waffles and that sort of thing come to the diner as a "just add water" mix.
Which brings us to the primary problem... A diner simply wont function without running water for more than a few hours.
Most restaurants don't carry large stocks of bottled water, and even fewer carry other bottled beverages. Sure you may have a few gallons of fruit juice, but soda will probably come from a bag-in-box dispenser (wont work without running water) the coffee machine is likely plumbed in and the tea most likely is as well.
So... If you had a staff of 6 and say 12 customers at the time of transport, all of the water you have on hand will probably be depleted within a day, maybe two days if you rationed carefully and didn't use it for making waffles.
Sorry to paint such a bleak picture, but on the up shot you would probably have enough food, even without refrigeration to last a few weeks.
Keep in mind that commercial freezers are really well insulated and inside a typical diner freezer you would find a near solid wall (a few feet thick) of frozen food.