Sure, if you are willing to demolish the old drywall and install new drywall.

You do not need to remove all the drywall, just enough to drill through the studs and pull the cable.

Patching is rather easy after a little practice.

The only real 'gotcha' is if the wall is textured.
Matching textures can be anything from simple to a real PITA.

You can cut out a panel about a foot or so wide for access. Then replace that panel with a patch after you are done running wire through. It is very similar to the procedure detailed in the link below.

Here is a link that might be useful: Drywall Replacement

If you take out the entire wall (or partial) add insulation in none exists.

" in my unit " - do you own an apartment building or are you renting a unit? If you are a renter, I assume your landlord would have something to say about this.