Replacing original sole with rubber sole. Complicated?

Usually only the part of the sole which contacts the ground gets replaced (it ends up about the front half of the length of the sole), but I'm sure they can cover the whole sole if you want them to.
 
the sole isn't usually actually replace either, but rather the new rubber sole gets put on top of the existing one.

it won't make a difference in terms of comfort if you're thinking it will give you more padding, but it does make shoes less slippery so that can make it more comfortable to walk.

and yes, along with replacing heels, this is probably the most common thing a cobbler does.