Is it possible to max-out Health, Shields, and Salts in Bioshock: Infinite

No I'm afraid you can't. There is no such option in any of the menus, not even in the PC version. I searched around a bit, but for this game this isn't an option.

Also, if you read some articles you'll understand why. Just a small excerpt:

The thing is — and this is possibly a spoiler — you’ll use your face-ripping, flesh-melting, eye-pecking weapons and powers to take out white supremacists. That’s game violence put to good use.

Infusions level up the health, salts or shield up to level 10 each. They do not add any other qualities besides making your bars bigger so you can take more damage, use more salts and have more shield . You can find vigor boosts that let you for instance use less salts for possession ....