You certainly COULD do what you are suggesting but I think it might be a bit bulky, particularly in the corners depending on where a seam lands and trying to miter those corners of the binding. You would have to sew all those squares into a strip first. If it were me, I would then press all those seams open to help reduce the bulk. AFTER you have quilted your sandwich, attach the binding. I normally folding strip in half - wrong sides together - and then sew with raw edges to the outer edge of the sandwich to the front of the quilt sandwich and then handstitch the folded edge to the back.
Before sewing all those little squares together, measure your top (top edge plus side edge then multiply by 2 to get total inches of all 4 sides then add about 10-12"). Then count the squares to see if you have enough of them to go all the way around your quilt. And don't forget that your finished size of your squares will be 2" once sewn into the strip.
As the saying goes 'it's your quilt and there are no quilt police'!