It's a great idea! I have done it, and it is a *lot* easier than straight-line quilting. I used a walking foot, which was really helpful both in terms of keeping the layers together and helping me keep the curves loose. I actually prefer these wavy lines to straight lines for many quilts. The wavy lines end up with a much softer look to them. And, it has the advantage of being a very easy way to quilt.
It's best not to do a grid; just lines all going in the same direction. As soon as you do a grid, whether the lines are straight or wavy, you run into the problem of tucks and puckers where the lines cross. While this issue can be overcome, it's one that you want to avoid until you are sure you know how to avoid the problems.