Does it matter where one installs an FSDT airport when installing for P3D?
Yes, they will run ONLY if installed in the folder our installer will place into. That's why we have an installer, and that's why you cannot choose a destination folder: because you are not supposed to change it, and the installer automatically select the only correct choice.
I ask because I recall hearing one can avoid having to reinstall them if they are installed outside of the P3D folder. True?
I'm not sure what do you mean with "avoid having to reinstall them". You mean when UNINSTALLING and REINSTALLING the sim from scratch ?
There's nothing you can do do avoid having to reinstall them in this case, the installation is not just copying files, it also downloading stuff, patching files according to the version of the sim, create config files on the fly for them, check registry entries and set permissions and a whole lot of other things to fix possible errors. You MUST always run the installer.