They are not correct, 걸어가다 is a combination word of to walk and to go - "걷다" and "가다", so it literally means "to go by walking." It differs by the verb to walk by specifying there is some start and end destination.
That would be 그는 집에서 걸어요.
As previously mentioned in the comment above, the 가 in the 걸어가요 makes the difference.
This is what I understand:
걸어요 means walk.
걸어가요 means walk+go, with the 가 indicating that he is leaving somewhere.