Thanks! Well tbh the basic log cabin pattern is pretty easy and so you wouldn't need anything fancy to make the outside bits of the blocks - you'd need to cut fabric strips, though, or buy them ready-cut. You can get 'jelly-rolls' (pre-cut strips) which would make life a lot easier. Then you sew them together on the machine, which you already have. So it's the middle blocks that would take the time, really.
Just from a cursory look at the tutorial, I see they say that lots of them can be done by hand-sewing, so they would certainly be possible. Things like the shirring might be easier with a sewing-machine. It's a question of whether you want to spend perhaps a lot of time on those centre squares, though!