Not at all my experience. Interruptions when designing is, to me, almost free. It's a completely different mental process at work compared to programming. One which does not need much wind-up time at all.

I wouldn't say creative work and "create new things that don't exist yet" is what's defining for expensive interruptions. Rather, whether you need to keep a lot of stuff in mental cache or not. That is not true for a large subset of design work.

Edit: My personal experience is that interruptions during design work is, in contrast, almost welcome. Once you come back to your designs after an interruption you often see things in a new light and catch stuff you previously didn't see.