"They can frown but they cannot stop you."
In California they can - and will - stop paying your benefits. A week or two week vacation that you'd planned in advance and can prove that you can probably plead your case. But a month or more? You need to get your "ducks" in a row regarding that. Each state varies. I had a friend visit last year for just a week who was on unemployment and he had his situation "covered". No loss of benefits. These days you can never be too careful.