I wouldn't do it with rats, for a couple of reasons.
A: It's extremely hard to get the correct measurement and correct vitamins for a rat's needs. Usually there's extra stuff in liquid vitamins that are either not needed or actually toxic to rats in the wrong dosages. And of course, you can't guarantee they're getting the correct dosage in a water bottle.
B: (More importantly) rats are extremely xenophobic with new things, especially food. If their water smells or tastes funny, they will often actually quit drinking it and get dehydrated. I've heard of them actually dying of thirst before they'll drink from a source they don't trust/like. By far, the most cost effective and easy to manage way to monitor their vitamins is to provide an all inclusive high quality lab block. I use Harlan Tekklad, which is the best available in the US. It can be bought from Mainly Rat Rescue, and a couple of other supply places. I also buy it in bulk under its commercial name Native Earth on Amazon. The price per lb. there is the best I've found after I figure shipping costs.
This is the guide I use for feeding my rats, and it has a lot of alternatives:
Yeah, I agree with Storyseeker. It's a better idea to just give them food rich in nutrients/vitamins than to try to mess with their water supply. The last thing you want is a rat who's afraid to drink water.
Huge no-no, something that petstores tell you to buy, or a terrible vet tells you to get.
ALL vitamins should be supplied by the diet.
Beyond what the others mentioned (tainted water supply, inconsistent "dosage") there is also a couple more things...
Unless you wrap your waterbottles with something to keep it dark, the vitamins become inert very quickly when exposed to any light.
You need to scrub out your waterbottles every day when putting anything in water and put in a fresh supply. If you don't the stuff that is supposed to be helping your rats could cause a bacterial infection.