Adobe programs will NOT install to an external drive... as is PROPER because when you remove a drive you have just destroyed the links to your operating system
Move data files to an external drive to free up space
I am not sure the OP mentioned installing. Maybe he meant just downloading.
Also I think you can install Adobe products on an external drive, yes of course they will stop working when the drive is removed or when it is plugged back and the letter changes (in Windows). However it has to be seen if the installer allows this to happen at all.