I'm not sure about there being research for switching between questions in a form per se, but there is certainly plenty on general page load times which still applies a little in this situation. As you probably already know, the short answer is that people get frustrated very quickly and if they can't do something as quickly and as easy as possible they will move on. So in general it's best to avoid any sort of artificial delays, and sometimes that means cosmetic "sugar" that gets applied to web pages.
My personal opinion on your scenario is from a visual standpoint, some sort of transition between questions is OK as long as it's not over the top. A very quick fade or horizontal / vertical swipe is fine and creates a better experience than just an instant switch. But I would say it has to be quick, 400ms is fine but even extra milliseconds that might be deemed unnecessary can be picked up by a user and can become frustrating.
I wasn't sure from your question if your delay was 400ms and then the fade or if that timing was the actual duration of the fade? If it was the former then I would absolutely shy away from adding any artificial delay to slow things down further. If there were any additional network or system issues from the user's side then you would just be adding to it.