Yes, but rarely. Coworker today is often one word despite beginning with "cow." It is much more likely unhyphenated than the similar word cofounder. The word co-owner is even more resistant.
Yes it should be hyphenated: co-worker.
In the US, coworker is normally not hyphenated. However in the UK, it is usually co-worker.British English and U.S. English Hyphen UsageThere are some differences in the manner in which the hyphen is used in the United Kingdom and in the United States, although these differences actually are rather minimal. For example, in the UK certain prefixes will be hyphenated when they will not be so separated in the US. For another example, the word preschool in the US is hyphenated pre-school in the UK.
Hiring that coworker
ex-coworker
It is not hyphenated.
ex-coworker
My coworker got promoted before I did.
No it's not hyphenated.
Motorcycle is not hyphenated
words are only hyphenated when they have a separate meaning when separated than they do when hyphenated
coworker's paycheck
Yes it should be hyphenated.