Generally, yes, but for others reading know your state rules. For example, in NJ working 32+ hours per work even if you earn less than you're weekly benefit amount, you are not considered unemployed and you get nothing. In NY, working just 1 second on any one day in a week, and you just lost 25% of your UI check. Do it 4 times in a week, and you get nothing. In AZ, the exclusion is only $30/wk. With $4/gal gas, no FICA on UI benefits, and possible child care, you can end up netting less working that PT job than if you'd just kept looking for the right job.
Understand that for most full-time workers that find themselves unemployed, part-time work would be unsuitable, and you can ligitimately refuse it provided you don't make a habit of applying for it. However, there are employers that advertise the perfect job, you apply, and at the interview they say, "it's going to start part-time then go full-time." You should run for the hills, and just say, "call me when you have a full-time opening."
UI and PT work doesn't mix well unless you really understand the system and all the ramifications.

