Should I publish work from my undergrad now that I am in graduate school and no longer working in the same field?

The experience of having gone the whole way through the publication process is very valuable and will benefit you when you start writing up your new research. In the long run (say by the time you'd be applying for tenure-track jobs) having a publication in another field won't help your CV much because people are looking at your research program. But in the medium-term if you apply for postdocs you may not have many (or any) actual publications (given the time it takes to write-up and submit research) and it's going to make you look better because it shows to potential supervisors that you're responsible and capable of completing a project.

Yes. Future employers in general like a longer publication record. (You also may end up working in another field or fields from that of your degree.) It also helps to go through the publication process.