there are some pretty old tied quilts around- so i would have to say-if done correctly they hold up just fine-
many are done with regular cottons, flannels and /or wools
choosing the correct batting is important- you want one that says 'good for tied quilts' or one that allows up to 10" between quilting lines (like warm & natural)
and you want to baste well- and make your ties every 4" in a 'grid-like' pattern- the (normal) rule of thumb is:
you make a fist and place it- a tie should be touching your fist in 4 directions-top, bottom each side.
use good quality (tieing material) some people used perle cotton, some embroidery floss (all 6 plys) some use some sort of yarn-
shrinkage depends on lots of things- the fabrics (pre-washed or not?) chosen batting, the fabrics themselves....and the way it is laundered....just like any quilt.