UPDATE -- THE GENERAL ASSEMBLY ELIMINATED THE LOOPHOLE DESCRIBED BELOW. Severance now usually disqualifies you from receiving unemployment.
The answer: it depends. Here is a direct quote from the DLLR Employer's Quick Reference Guide (see page 19):
The receipt of severance payments will not be deducted from . . . benefits if the individual’s job has been abolished through layoff, facility closure, etc., unless the employer continues to pay all wages and benefits, including leave accrual, after the individual has physically stopped working.
Translation: Severance will not be deducted if your job was abolished when you were laid off unless during your severance period you are receiving ALL of your wages and benefits and are still accruing leave.
Nevertheless, be careful to answer of all the DLLR's questions about severance benefits truthfully, and disclose severance benefits whenever asked.