Would teeth improve in strength if one was fed nutrients intravenously only?

If you take someone (early 20s) that has teeth with a very weak enamel and force them to take nutrients intravenously or through their belly button meaning they never have to eat for their life again through their mouth, would their teeth improve if they continued to brush with toothpaste?

No.

First of all, enamel doesn’t regrow or continue to grow - what you have when the tooth erupts is all you’ll ever have, it just goes down from there.

Second, teeth and their supporting structure being made of living bone and tissue, lack of use causes atrophy. It’s the mechanical stresses of chewing that keep your jawbone strong and your teeth in place. If you don’t use 'em you lose 'em - if not to decay then to bone loss after which they loosen and eventually fall out.

Enamel doesn’t regrow. Minor cracks can be repaired with flouride or novamin, but you can’t rebuild it wholesale.

Having said that, if you aren’t exposing your teeth to acids in foods or the trauma of chewing, and the bacteria in your mouth never have any sugar to eat, then one would assume your teeth would age pretty well.