Just about ANY quilt can be done in that time. The real question is how much time do you have to devote to piecing, quilting and binding a quilt over the next four weeks?
Just viewed that tutorial you referred to,
https://www.youtube.com/watch?v=mgwM...EF21A981F69C28, and the final block looked a little choppy to me. I've made this quilt before and never remember it being so...not smooth.
If you have the time to devote to this quilt, I recommend you find a different pattern for it. It can be a beautiful quilt that's smooth. Maybe this one;
https://www.youtube.com/watch?v=gkIu-HnS_oQ
Good luck with your decision.