Not necessarily, but this may change in the very near future! Currently, individuals may receive unemployment benefits even if they have been or are being paid severance, as long as the severance is not viewed as extending employment.
For instance, an individual would be disqualified from collecting unemployment for any period of time that severance was paid in lieu of notice (example: when an employer is contractually required to give 60 days prior notice of termination but instead terminates without giving any notice and pays severance for the notice period).
On the other hand, a person receiving severance payments based solely upon years of service is allowed to concurrently collect unemployment benefits. This may change in the very near future. In May 2012, a bill (A2654) was introduced in New Jersey to disqualify an individual from receiving unemployment benefits if they are receiving “severance pay” in an amount that significantly exceeds the statewide average annual or weekly wage.