Can multiple cores be used by PostgreSQL to run code in sections (cursors) of a table effecting parallelism?
Actually, PostgreSQL 9.6 can run parallel (read) queries. Parallel writes aren't supported yet.

The approach you suggest would work, but some care would be required to ensure it was consistent, since each cursor would be a different session with a different snapshot of the database.

You could instead just run 10 UPDATEs from 10 different clients. Same effect, simpler, and probably faster. Just make sure the targeted row ranges don't overlap.