Learning proprioception definitely improves hand/eye coordination. Before I started VRT, I had to spread my fingers apart, each onto my desk top, and close my fingers until they connected with the pen or pencil I was trying to find. Post VRT, I can simply reach down and pick the pen up without hesitating. It has also helped a great deal in the kitchen, where I no longer chop my fingers instead of the veggies!
When you start VRT, you may think it's not going to help, that it's a silly thing to do, that it's too simple to work. All wrong! I guarantee that, if you try VRT and work on it (really work, not just sorta do it), you will begin to see improvements within a couple of weeks, and much greater improvement after a month or six weeks. Again, you only need to do the formal exercises until proprioception becomes natural for you. At that point, you need to remember to use it every day, do a little walking in the dark (or with your eyes closed), but it is a tiny price to pay for the improvement in how you will feel.
Also, 30 years ago, it was believed that you couldn't benefit from VRT until your condition was stable. For Menierians, that meant not having crises. When Meniere's struck again, turning my situation into a bilateral (both ears) one in May, I have been thrilled that I'm not having serious balance issues. I have ramped up the VRT to compensate for the increased imbalance, but I've been able to do really difficult instream work for our fisheries agency recently, even climbing algae-encrusted boulders to get above a waterfall, over a huge slide comprised of clay that's almost as slippery dry as it has been wet. Most PTs now agree that you can't wait in the hope of getting better before starting VRT–it is the way you will get better. If only I had known that 30 years ago, perhaps I would have escaped four years of creeping around, perpetually afraid of falling, never knowing exactly where I was or where other things were.