"Pick up," you say. But you don't think you're going to learn Greek that way, unless you spend a lot of time speaking and listening to it. And unless you're going to marry your boyfriend, you're not going to take a course in Greek, are you?

The reasons for why not are in the replies above.

Languages can be fun, but not necessarily for everyone. If he wants to learn it because it'll be fun or it'll broaden his horizons, then he probably should.