I'd like to say "No, you don't" because my degree is in music and I've taken two classes on computers in my life, one on programming the Apple ][ in 1984 or 1985 and the other on typing in 1991. If you're self-motivated, it's pretty easy to pick up the details as you go along.

Of course, it does help to know how a virtual machine works. Learning by osmosis isn't terribly efficient, though it's likely you'll have to learn how Parrot works by osmosis even if you did have a background in compilers.