Is this a grammatically-correct sentence: “Vote as if your neighborhood depends on it”? Or would “depends upon” be better?
If it were my slogan to the masses I would make it:
“Vote. Your neighborhood depends on it.”
Avoids the issue altogether, especially worrying about whether the construction around a subjunctive is technically correct but loses the appeal to the polloi.
Wilson Follett “Modern American Usage” (1966)
*In this case, the prepositional phrase “on style” is linked to “word,” but “upon style” is linked to “effect.”
I’m going with “on.” After all, who ever said, “Grandpa has Depends upon?” 
As a professional editor, I’d let an author use either “depends on” or depends upon" depending … er… on their personal preference.
But if I were expressing my personal prefererence, in this particular situation I’d vote for “depends upon.” Why? I dunno, sounds more serious to me that way. If you google (using advanced search) “depends on” vs. “depends upon” you will see that the former gets far more hits, but you can instantly see that the latter gets serious, literary kinds of hits (like “so much depends upon a red wheelbarrow”). IMHO it has to do with how it falls on your ear … de-PENDS u-PON is very nice.
I checked the American Heritage dictionary, and it was neutral, saying “on” or “upon” either one could be used without specifying situations.
When I checked the Oxford, however, it listed only “depend on” and “depending on” as phrases. No mention at all of “upon.”
When I proofread mss., I judge such arbitrarities by context. If the author writes “on,” I’d leave as is, as the preferable usage. If the author writes “upon,” I’d give it a little more thought. “Upon” strikes me as slightly more precious, even British. So if that were appropriate to the text, I’d leave it. Or, if rhythm and flow is important to the audience, and subtracting the syllable disrupts that, I’d leave it.
It does me, too, so I was surprised that the Oxford listed only “on.”
Although the OP didn’t ask about this specifically, if you don’t use the construction Chief Pedant recommends (which I think is better), I would write “Vote as if your neighborhood depended on it,” not depends.
“As if” creates a contra-factual condiition which properly takes the past subjunctive mood, hence “depended.”
Oh and, since it’s a grammar thread . . . your OP contains an extra hyphen.
Part of the issue for me was having the punch of a slogan lost for the sake of grammatical pedantry.
The specific question in the OP is adequately addressed above but the unasked question is whether there is a better way to phrase the slogan…
For a neighborhood which needs slogans to help it get out the vote I think “upon” is a bit stilted, and when I thought about the proper subjunctive construction it seemed even more so. I admit to making an inference about the neighborhood in question, but that’s the practicality of creating a good slogan.
I’d concentrate on (or concentrate upon) the word “depends.” You’re wanting to use “depended,” i.e., “Vote as if your neighborhood depended upon it.” It’s one of those subjunctive mood thingies, as mentions commasense.
In my mind, they have slightly different meanings –
-
“Depends upon” means “relies on” – Your family depends upon you to attend to your responsibilities. Your company depends upon you to do your job.
-
“Depends on” means that the answer to a question varies based on differing circumstances. “Whether you will be promoted depends on your job performance.” “Whether we go camping this weekend depends on the weather being good.”