That would probably work, but controlling the rack with your hand while climbing might be a little awkward and "touchy". You'd need to play with adjusting it. There's also a variation of this shown in On Rope, but it uses a weight hanging below the climber - you'd have to check it out to see how it works.
Personally when I set up a climbing rig like this, I use a Troll Allp descender. This is a true controlled-rate (aka variable-rate) bobbin-type descender, with a little butterfly screw to finely tune the friction applied to the rope. Unfortunately these descenders (made in the UK) are fairly tough to find.
In lieu of an Allp, you could try starting out the usual way with someone else feeding the rack for you. Once you've figured out the optimum rate of rope feed by ONLY adjusting the spacing of the bars, you could make a mark on the frame and install a small screw clamp to fix the bottom bar in place. I've never seen this done or tried it myself, but I don't see why it wouldn't work - assuming the rope is carefully flaked out beforehand.
Have fun.