If you want to be able to enter the world of Deaf people, I would say yes, you should learn ASL. It will enrich your life in ways you couldn't even imagine. To have a conversation with someone without using your voice, but your eyes and your whole body is an incredible experience. Little did anyone realize that they could access this culture living within another culture. Deaf people are Americans, but they have their own subculture. They think and react a little differently to some situations.
Learning most languages is a difficult undertaking for most, requiring lots of memorization and study of grammar. ASL is much easier than that in some ways because the grammar is simpler, but still different from that of English. It is more difficult in other ways because you are taking in language through your eyes and that is a strange but exciting sensation at first.
Visual languages have great advantages over spoken languages. For example you can be at a very loud part and if you know how to sign you can easily converse with someone else who knows how to sign and the surrounding noise won't affect you at all. It is also convenient for when you are a little bit far away from someone where normally you would have to shout. If you can see the sign you can understand it. No shouting is necessary. It also comes in handy in the rare cases when you are in two different cars and you are close enough to sign to someone else in the other car like "We need to pull over at the next gas station, we're almost out of gas."
Amo, Amas, Ama, Amamos, Amais, Aman. I've got very good news for those of you who dread conjugations; there is no conjugation in ASL. So you learn one form for the verb and it works for all of the persons and tenses. Now isn't that nice? The signs are iconic and that means that a high percentage of signs look like what they mean, so that makes them very easy to remember because they fit into your memory very conveniently.
You are never too young or too old to learn and you never know who you are going to meet in life who will be a deaf person or another person who signs. So don't just stand there, get out and learn ASL. You'll be glad you did. And some deaf people will get to know you and that will be nice for them. So go have some fun. Learning language is fun and it opens your mind and expands your horizons.