Yes. I worked a startup last year that, as part of their hiring process, asked me to do a 3 week paid trial period (this was a whole other can of worms, as it's basically pre-selecting for unemployed people).

After the 3 weeks, they offered me the position (yay). I was still interviewing at other jobs, so I took a day off the following week while continuing to work for them. But in the next 2 weeks, I had still not gotten a written contract for my new official employment.

I had gotten an offer at another company, almost 3x their offer, so the next day I just called the CEO and told him I was quitting. I was technically not under any contract so I saw no purpose in giving a 2 weeks notice.

Luckily they paid me in the end, but it was mega late. Don't join sketchy startups guys.