I wouldn't consider myself a goat expert by any means; I did have dairy goats for a few years.
Most likely the goats would do "okay" at least for a while, probably gradually declining over time, but supplementing grass with grains, etc and alfalpha would be desireable for their long term health, particularly if they are dairy goats. Additionally, the soil in your area may or may not contain (or contain too much of) certain things goats need to do well, such as selenium. I would recommend that you find someone LOCAL who raises goats (your county extension agent may have info too) to get a better feel for the local needs.
Goats are quite different than sheep; they prefer to browse and I found that pasture grasses was about the last thing they reached for.
It would be worthwhile to get a good goat how-to book to understand their requirements and talk to a local to see how your area meets/doesn't meet the requirements.
Good luck, they are a lot of fun. I had a fallen tree for a while at the same time I had some kids. Talk about a hoot watching them play king of the tree! And you'll need a good fence!