I know I I get sent back to a Vita-Chamber. But does anything else bad happen? If not, it seems like when you're near one, you're better off dying than using a first aid kit. I feel like that's probably not correct. Is dying really so painless?
As both Jason and Joshua commented, there is no penalty to dying in bioshock 2.
It kinda ruins the feel of the game but when necessary it is great to have to save a health kit as you referenced.
If you need more information I'm sure I could dig up some other locations that have information on this for you to read through.