Is it possible to fix bowed baseboards?
Base shoe molding is really rather flexible and should be able to push up to walls that are more than an inch or so out of alignment over a reasonable length of say nine or ten feet. 

You did not show any picture or quantify the amount of bowing that exists so it is hard to take the shoe molding fit any farther without more information. 

Normally when installing shoe molding it is nailed with just short finish nails into the baseboard. You do not attempt to use huge nails in an attempt to reach through into the studs. For cases where it seems that you are trying to nail the base shoe into a spongy surface I have found it to be useful to fasten it in place with a pneumatic brad nailer. The nailer imparts a lot of energy directly onto the brads so that they drive home without the bouncy flex of a wall section being much of an issue. 

The bouncy and unsupported wall sections may very well have to be left for a discussion on another day.