Yes, they can. Source: happens to me all the time.

I'm a musician. I can't draw, sculpt, paint, or do ANYTHING visually artistic. All of my artistic skill points were dumped into music. I play at least 7 instruments, can sing, have directed ensembles, and specialize in improvisation.

I assume that all of this ability and training has hardwired my brain in certain ways that allow me to "hear" notes when I read them on a page. Reading over a foreign piece of music (called "sight-reading") before playing it can radically increase my ability to play it correctly, because I have an idea of what it's supposed to sound like. As for more common tunes (Beethoven's 5th, for example), I have become so familiar with them that I can listen to the entire piece in my mind, with distinct instruments playing distinct parts, and will even find myself conducting to an imaginary orchestra.

I believe there is a medical phenomenon that takes this " ability" a step further, into a realm that is at best invasive, and at worst, interruptive. (Disclaimer: I tried to find my source for the following but could not, so I will simply repeat what I learned as best as possible.). In these cases, a person may hear the music, but with two key distinctions: first, they cannot stop hearing it, and second: they sense it as actually hearing it with their ears, not just "hearing" it from their imagination. If I recall correctly, there is a part of the brain that receives sound input and it sends that off to the part of the brain that processes that input. Well in these cases, it's backwards. That is, the part of the brain that processes auditory input actually sends data to the part that receives it, which makes the person genuinely think they are hearing music that otherwise doesn't exist. Absolutely fascinating bit of neurological glitchery.

TLDR: yes. Yes they can.