You absolutely can however if you have empty conduit already in the wall going where you want it, it will be much easier to run it through that.

You don't need conduit, although if you're running it through something like a cold air return I believe you need Plenum rated cable. For both my current and previous house I used existing in-wall runs of coaxial and/or telephone lines to run ethernet. Just pulled the cover off, cut the cable, taped the ethernet to it and went into the basement to pull it through. Mind you, I didn't have a lot of bends to deal with, and we ditched landline and cable years ago so we didn't care about the existing lines.