As mentioned above: It probably does not need replacing but if so, it isn't that hard and way cheaper to do it yourself.
Not mentioned above: Your question ' Can I use the TT without the toilet?' Don't be so concerned about the 1/2" hole so much as the great stinking 3" hole in the floor. IMHO no you can't use the TT with the toilet missing.
Marsland mentioned installing a shut-off valve behind the toilet. Good idea. You can shut the water off to the toilet and (with an adapter) connect your toilet wand to the shower hose when flushing. You don't have to drag a separate hose in the door, down the hall, etc. Some have installed a 'TEE' with a separate valve behind the toilet and attach the wand there.
Stu