I am undertaking a bathroom remodel and lo and behold found some water damage against an interior wall. It is not extensive and doesn't run through the entirety of any of the studs or plates. I'm thinking I should be fine with a wood putty repair rather than replacing this but appreciate a second opinion from someone more knowledgeable than myself.
I agree that you could make a repair rather than replacing the bottom plate. I would recommend the 2-part repair putty (it's like auto-body filler) because it bonds better, is easier to shape, and can be nailed/drilled/screwed into without crumbling so much.
Ensure that all rotten wood is dug out/removed. I use a product by Minwax called Wood Hardener prior to using the filler in situations like this, it soaks into surrounding wood fibers and firms them up and helps prevent further dry-rot.