있어 in 얼마 안 있어 is similar to 지나다. It is another common meaning of 있다. 얼마 is an indefinite small amount of something, similar to "some" in English. You can think of the time-related phrases like this (they are all commonly used phrases). - 곧, 바로, 곧바로, 바로 뒤에, 금방 = immediately, (right) then, in no time. - 얼마 안 있어(서)/지나(서), 얼마 있지/지나지 않아, 조금 후에/뒤에, 조금 지나(서), 조금 있다(가) = before long, after a bit. - 얼마 뒤(에)/후(에), 얼마 있다(가), 얼마 지나(서) = after a (short) while. - 한참 뒤(에)/후(에), 한참 있은/지난 뒤에/후에, 한참 지나(서), 한참 있다(가) = after a (long) while.

Well, it definitely sounds natural. There have similar meanings, but I think you use "얼마 안 있어도" in situations where you start something, and you are watching the clock to wait for something to happen. Something like, "Go and try this new ergonomic chair that I just bought, and "얼마 안 있어도" you are going to feel this horrible pain in your back" (something like, "in no time...").