Does a transmitter's "model memory" include radio binding?

Thanks to the help on the "choosing a transmitter" thread, I bought a FlySky 9X from Amazon, then used the programmer board from SmartieParts to flash on the er9x firmware. (I didn't hear about HobbyKing's 9xr until afterwards, that might have saved me some money and hassle.) After a few days getting used to my first serious (not packed in with an RTF) transmitter, I find I'm a better pilot and my Syma X1 gets much much better range.

I'm about to use the included receiver in an Arduino project, and before I started, I was curious: does the radio binding get stored in a transmitter's model memory? Or will I have to re-bind the radio every time I switch between the new project and my old Syma?

(I guess I'm specifically asking about my 9x controller, but more generally is that a reasonable expectation?)