Yes, but you can speed up the process a lot by learning from others. There are many great harmonica tutorials on youtube, for example. Different teachers work on different styles of playing and different genres of music, but the most common is blues harmonica.

With regular deliberate practice, you can expect to be playing simple pop tunes within around 3 months. Within 6 to 12 months, your technique will improve and you will probably be able to work on bending notes (a very important skill for getting the best out of a harmonica).

The harmonica is a small, portable instrument that is easy to pick up and play. However, it can be surprisingly difficult to master. This is because the harmonica requires a great deal of breath control, coordination, and embouchure mastery.