I can't speak for your state, but here, the amount of people on unemployment and how long they are affect the future unemployment tax for the company. The more that collect, the higher their rate will go. That rate is on all of their employees, not individuals. In the past I've had an employer choose to just pay me for a couple months of not doing much rather than having me go on unemployment and it affecting the entire company.
Ultimately, I think its a conversation you should have with your employer. I'd never go on unemployment without discussing it with them. If they aren't happy about it, when they get the notice, they can report that you turned down work. Then you may not get unemployment, and may end up actually unemployed. It may not be a big deal to them at all, but you absolutely need to have that conversation with them.