I learned this the hard way in college. I got accepted to a summer startup program for an idea I had (it wasn't quite an incubator but more like a think tank course, where you got a stipend to work on your startup idea). I thought I could work on my startup, meet all the requirements to stay in the program, and keep my full-time job as a developer at another company.

I was able to do all 3, and thought it showed I was a real hard workin' go-getter to have a full time job and a full time startup I was working on. Until the startup program coordinators found out I was working a job along with my startup and almost kicked me out of the program.

It was then (actually, years later) that I realized I wasn't doing 2 jobs full time; I was doing 2 jobs part time, and that what makes the people who can run a successful startup while working on a career exceptional is just that, they're exceptional at both.

I think a lot about how much further I could have gotten with that startup if I had just quit my job and actually worked full-time on it, especially given that the program paid a stiped, instead of trying to sneak some code in whenever my boss wasn't asking for something else.

So I wouldn't say impossible, but really tough for anything big enough to be its own business.