No.

Unemployment benefit is just a type of insurance, not related to US Government assistance (not public charge). It is just like other types of insurance, the employer pay the unemployment insurance premium for you every month, and thus once you are laid off, you will be paid the unemployment insurance benefits as long as you have the legal right to work in US such as US citizen, green card holder or EAD holder, etc. It will have no any negative effect on you in this case.