Will Pokemon Go work with my rural location?

So long as you are able to receive Mobile/Cellular Network Data and GPS, you should be able to wander around collecting Pokemon perfectly fine.

Also, depending on your village, there may be one or more of:

• PokeStops, which give you items like Pokeballs and Potions (and can be temporarily buffed with Pokemon Lures to attract Pokemon)
• Gyms, which can be captured, trained at and fought by members of the three Pokemon teams (Red, Blue, Yellow). You will be able to join a team at level 5.

You may be able to check this without downloading the game by using an Ingress Intel/Portal checker (as Pokemon Go is based on the same locations), however note that currently not all Ingress portals are Pokemon Go spots.

No you will not be fine. I live in the States and I cannot get pokemon unless I go to a city. I can walk five miles and not find a pokemon or any gyms or pokestops. The only way to get any fun out of pokemon go if you live in a rural area is to stock up. Go to the city and grab a lot of eggs at pokestops, you can still hatch them in rural areas and it gives you xp. But you won't level up as fast as city players, also you won't be able to get pokecoins from gyms on a regular basis because there might not be any near you.

Pokemon GO bases the majority of spawn data on where humans are likely to be. Therefore, rural areas with little to no tourism will have rather few spawns, though they will still get the occasional odd spawn.

You may artificially boost these spawnrates through the use of Incense, but this is often cost-prohibitive due to the amount needed to match 1km² of a heavily populated area.

Whenever you are in a relatively urban area, you should really consider getting as many items from Pokestops as you possibly can.

I also live in Portugal, in a small village, and I had to go kilometers upon kilometers to find one Rattata, because that's what it took for the game to get my location. If you go to nearby, bigger towns, or even villages, you might see some Weedle, or something, and rarely some Pokestops.

Dude!!! You should be fine. I live in Zimbabwe (I hope the devs aren't reading this) and I've driven about 100km in a radius around where I live. I've managed to find 5 gyms and about 15 poke-stops. Check out churches, or anything with national/historical significance. However, it would be nice to have an option for those of us off the beaten track to at least suggest/request a few more spots.

As far as pokemon go, I've found more in towns but still find them out in the country. You seem to find more as you level up. Just catch everything you can as often as you can and more and more will start showing up.