While this whole situation is really silly, your question is worth considering. Please understand that I’m answering it from a “knows slightly more than an utter layman” perspective (That is, I am not a lawyer so please do not use my remarks as legal advice), but… I think most of this is sensible.
As you know, 911 is specifically for “I need help right now but I’m too stressed/panicked to remember the normal emergency phone number” situations. Unfortunately, there are those who think 911 is the number you dial to get a magical genie in a state uniform to grant your wish here and now. The state generally disagrees with this interpretation and so does pretty much everyone else who doesn’t call 911 over a fast food burger. So this is the primary offense at hand; he used limited emergency response resources over something that isn’t even remotely close to an emergency. While this part is obvious, I mention it to establish context.
As for whether he would have still been arrested for dialing the police at their direct/non-emergencies line… that’s a really good question. In theory? It can be an arrestable action. In practice, most departments are not going to go to the trouble. They will probably tell the caller this is a civil court matter at most and hang up. In most situations that will be the end of the matter insofar as the police care. However, police in most locales have very broadly defined arrest powers (Edit: previously said ‘problems’ instead of ‘powers’; bizarre typo) and may detain someone for almost any reason they care to come up with… I’m willing to bet a court would be sympathetic if the police sent an officer over to arrest the caller, claiming his call was knowingly frivolous and constituted ‘obstruction’ or any even vaguely similar charge, for example. So this really depends on how much one feels like tempting fate, and how fickle the police are that day.
So let’s say our theoretical burger caller finds no police response is forthcoming. They can do that. If they think the situation is likely to be a colossal waste of their time, they’ll simply not show up (or if they do show up, it’s going to be for the ‘teach someone a lesson’ motive of arresting whoever called them). Where does this leave our customer? Well, technically it becomes a matter for civil court, but the damages are so trivial (what does a McDouble or McRib cost these days? I’m just going to say $5 is vaguely in the right ballpark) that no lawyer is going to take the case and chances are the court system will also refuse to hear the case because having a serious hearing/trial/etc. over five dollars is a flagrant waste of their time too. So any sort of litigation is right out.
Now to get to a two-fold conclusion. In theory, yes you can be arrested for calling the police on their non-emergency line regarding a burger. In practicality you probably won’t be (though to reiterate, my remarks don’t constitute qualified legal advice) unless you go out of your way to irk the police over this. A single call about it will likely be met with them dismissing the concern, hanging up, then having a chuckle and/or sigh about ‘that idiot’; pressing it is probably going to result in someone showing up for the previously mentioned ‘lesson teaching.’ Beyond that, you’ve probably reached the same realization everyone else has and were simply putting forth an interesting question (it was fun to think through, however!). That realization is simple: Residents of Sane Person Land don’t call the cops on any phone line over a disputed fast food burger; they just cut their losses, tell their friends that particular store sucks, and never go there again unless the management changes. Residents of Crazyland dial 911 over it, get arrested, deported to Sane Person Land, then give interviews to the media confirming that they just went back across the border to Crazyland afterward.