First, it's my understanding that you can run any opamp circuit on a bipolar power supply and this gives you more headroom (e.g., running +/-9V gives you twice as much amplitude swing as a +9V with a voltage divider giving you +4.5V as your bias point. If that's wrong, please correct me.
In practical terms, what does this really buy you? For example, if I converted my TS clone to a bipolar supply, what difference would I hear?
Is it worth the added components?
On a more practical note, to do a conversion, I hook everything marked Vr to ground, hook "ground" to the negative supply and V+ to the pos. supply, right?
You've got it about right. Don't forget power supply decoupling caps will be required across both rails to ground.
As to whether or not you should do the mod, I'm not sure - it may give you more headroom, but if the circuit has been designed to work perfectly well with a single 9V supply then you may not get any real benefit, but it's always worth experimenting.
given that a guitar signal is somewhere less than 1V peak to peak, the 9V version already has a tonne of headroom. I would say that it's not worth the effort.