The question should be: Are ukuleles real instruments? or is the ukulele a real instrument?

Physically:
1. You can see them, you can touch them, you can play them: They are real and not virtual.

Technically:
2. Instrument is a foreign word for tool. You can use it for batting back tomatoes, eggs, and foul vegetables - even cricket balls (but only once in most cases). And you can produce more or less harmonic sounds. Yes, as a tool it is also an instrument.