Obviously, yes, they can. However, is a wizard Proficient with an unarmed strike?
I was writing up a wizard for a campaign, and when I was going over them I noticed that they don't just get simple weapon proficiency, instead they have a list of weapons they're proficient with. Unarmed Strike isn't on it, and technically it is listed as a simple weapon.
At first I thought it didn't make sense, but when I thought about it, it kind of did. You're basically a scholar, you have almost no weapons training at all-Why would you know how to throw a punch? I know from personal experience, if you've never been shown how to punch correctly (or kick, for that matter) it's not just something everyone picks up.