First of all, the Yashica 35 series cameras are quite nice and I think it's worthwhile trying to get your camera working again.

Regarding your specific question, you can find helpful advice regarding battery corrosion in this camera here, summary: Use cotton swaps lightly moistened with white vinegar and lots of patience to clean out the corrosion, some pieces of paper and toothpicks will help with tricky spots.

After you have cleaned the battery compartment, generally, the only way of figuring out whether the camera works as it should is to put a roll of film in it and start shooting. In order to do so, it's probably best to carefully read the manual first, which you should be able to easily find on the internet, for example here or the 35 without the G should be quite similar.

One problem you might encounter is that the required batteries are not available anymore, however you will also find advice on replacements readily available with a quick Google search, for example you can use an adapter, but there are also more self-made versions. I think there are also modern alkali replacements for the PX32 with a slightly higher voltage, which shouldn't be a big problem in this case (but I can't vouch for it, as I don't have any first-hand experience with this camera).

As your camera seems to be in generally good condition, I would be hopeful that things work out fine. However, on a final note, another common problem with the Yashica 35 series is the "pad of death", which requires a slightly more elaborate repair (Google helps again).

This overview of the different models of the Yashica 35 series might also be interesting.