Yes it does. Apple isn't stupid-- they wouldn't design something that will burn out if you don't carefully compare the specifications of the charger you are using to the nearly identical looking one you had. If there was something you shouldn't do, they would tell you not to do it. Otherwise they assume that you will use the product how you want. They design stuff that "just works".
I don't know how the charger communicates with the computer. It most likely sets a voltage on the center pin that tells the computer how much power is available. There could also be a resistance between some pins. There could even be serial data sent, but that's less likely. The point is there are simple ways for the charger to tell the computer how much power is available. Maybe when I get a chance I'll try to figure out the sense mechanism.
This is a bit off topic, but serial data over the magsafe gives me an idea: why not run USB over the magsafe too, that way one plug would be all that's needed to connect the computer. They could put a USB hub on the magsafe brick which devices could be plugged into.