It is urban rather than suburban in character, but in the sense I think you are getting at it is a "suburb" of NY.

A hundred years ago I suspect that a town like West Orange would have been routinely identified as a suburb of Newark. Now such a label would be rare if not nonexistent - it is a suburb of New York. Newark isn't a central city any more.

The picture is complicated somewhat by legacies of the time it was more of a central city (Prudential; the older skyscrapers that are still around) and by the fact that it is the state's largest city and so attracts government involvement (e.g. NJ Performing Arts Center; federal buildings) as well as businesses that for legal/regulatory reasons are focused specifically on the NJ market (e.g. Horizon Blue Cross Blue Shield of New Jersey).

Of course it has its identity just as many suburbs have their own identity, particularly if they have been settled for 300 years. But I think over the last 100 years the growth of the NY metropolitan area has swallowed it up, with the process accelerated by middle-class flight from 1950, particularly after the riots.