You are describing a quilt as you go (QAYG) method. normally you would also cut the backing to size and quilt that in, then join, however, leaving the backing off and adding it at the end will work too if you can figure out how to get batting behind the sashing strips.
Here's a link to the qayg tutorials on this board.
http://www.quiltingboard.com/search....ou+go+&u=&s=10