Possibly, but 1) they had to GET to those planets in the first place, which requires that they know their way around a space ship and 2) "farmer" is not equivalent to "hillbilly", especially in the trekiverse where technobabble pervades everything from warp drive to pickled beets.
Tell that to Zephram Cochrane.
We can take the small Peregine/Fighters as a pre-existing design, which explains how Starfleet was able to modify them into combat roles for the Dominion War. But the Ju'day class would have been more effective in this regard, with its heavier armament, superior shielding and similar maneuverability (given that the Defiant class would have been the ideal but was too expensive to mass produce). Given this, we can probably take it as a safe bet that the Ju'day class was some kind of low-tech contraption assembled from designs from the Maquis equivalent of the Anarchist Cookbook, cobbled together from a collection of compatible though not always identical parts, most of which would be available at Qualor-II or a similar junk yard. It wouldn't take much: take four impulse engines, a warp core, some driver coils of a particular size (you can probably steal these from a freighter) and an engineer who knows how to rig the plumbing and electrical systems. It won't be pretty--and indeed, the Judays are not AT ALL pretty--but it'll fly, and if you can make your connection with your local arms dealer, it might even shoot.
