I'm sure this varies from school to school, but I will share our experience with you.
I think 3rd grade is not an issue, because it is easy to go back to traditional schools at lower grades. I think you need to be more careful once the kids are in middle school.
My DS was in a private GT school for part of his middle school, and it was a huge disappointment. The kids were supposed to work at their own pace. This works well only for kids who are strongly motivated. But for anyone who is not, there is little accountability and many kids there lacked very basic skills and basic work ethic. DS was very frustrated in an environment where everyone talked the right talk but the kids didn't learn anything. He did a lot of self study and was academically advanced. But when he came back to a traditional school, he did briefly have a tough time getting into the routine (following rubric, etc).
When we looked at the private school, we asked to see their students' work samples and the school refused. Some academic information that they gave us was also misleading (we found out later). I'd say you can ask to see their homework assignments, textbooks if any, student work samples, and maybe even standardized test scores if they have any.
