Hi, I came to piano after playing guitar for about 14 years. My reason was that piano could be a self-reliant instrument in making music whereas guitar sounded best in a group, and I was sick to death of having to rely on other (unreliable) people, in case you're curious.
Music theory will definitely help your guitar playing, it will give it direction. It's very easy to tell someone who doesn't know their theory, their improv is more or less random. One guy I met seemed to be just be wiggling his fingers and strumming as fast as possible. I didn't have the heart to tell him it sounded like crap. You probably know about wankery... It's just a case of musical maturity, the next level. It would be better if people started out like this, but the guitar community is saturated with immaturity.
I'd like to mention that theory isn't absolutely necessary, but it's a big step in the right direction - making your notes mean something.
...and piano is a great way to learn theory! The linear organization of the notes is easier to illustrate the concepts than on a guitar where you can play the same note in 5 different spots. Besides being a great intrument in itself, if you start learning piano you may be surprised how absorbed you can get into it!
You're probably not interested in learning to play 'mary had a little lamb' and hundreds of little diddies, though starting from such basics is useful in learning to read notation, so it could be a good idea to pick up one of these because they explain note values, and where the pitches correlate to the keys. They're usually graded, any will do - go find something that looks like "grade 1 adult beginner piano method".
You'll probably outgrow that quickly, so while you're at the store look for a theory book with a similar title to work through. Consider paying a teacher to check your work (and your playing!), not to mention the guidance/direction a jazz teacher could give as well. It may all be greek to you, but stick with it and before too long it'll become second nature, and the effect on your playing will be substantial. Take the theoretical ideas and experiment with them in practice, people will notice your playing means more, sounds better, has a wider range of expression.
If you're interested in classical I could give you a few book recommendations and a bunch of websites. Oscar Petersons advice was that classical music made a strong foundation for playing jazz.
Topic: Guitar through Piano