Is this said normally?
Is "Ist so wie schwimmen gehen, nicht?" correct? Or rather, is this (ist so wie verb + gehen) a construction used in normal, everyday German?
You know the expression"it is like riding a bike, you never lose it."in a similar case: "ist so wie schwimmen gehen, nicht?" = "(it) is like going for a swim, isn't it?" In fact the subject is missing, but that happens frequently in spoken speech. So the sentence seems correct to me. Your other question -narrowed down to verb + gehen -: "gehen" is often used in combination, but in general there is a period of movement, before the planned activity is engaged. f.i. "Ich gehe schwimmen" is said in a situation you have to go to the pool and then start swimming, "ich gehe schlafen" means, I am going upstairs and will sleep.