Absolutely you can. I don't use my system disk (C:) for any games at all. I have EA games from the EA-APP intalled across 2 SSDs.
Only the EA APP itself is on C:
If memory serves there is a default drive of your choice assigned, or it auto defaults to C: the first time, but it's easy to change install location, on a per game basis.
When installing it defaults to your default drive - in your case C: But you have to can confirm before anything starts, just change the intall directory before starting download. (It's easier if you set up a simple empty folder called EA games, or a name of your choice. That folder functions in a similar way to the normal C: drive, "program files" or "program files (86)" install folders. (I assume, but it just works.)
Game saves are often stored on C: but sometimes in the game directory itself. perhaps G: drive for instance. But none of that is important. All game files can be installed on any drive.
I'm a bit fuzzy on the default drive thing as I did that years ago, but for sure multiple drives are fine. I have "EA games 1" on E: and "EA-2" on G: Folders I set up and chose the name of before any installation. I installed the EA-App on my system drive.
(Not sure about external USB drives.)