Should I apply for out of state license before applying to jobs?

I'm a California new grad RN. I've applied to a number of out of state new grad programs and have gotten rejection emails from most. I notice that for most of the job requirements, it says "MUST BE LICENSED IN ______ or COMPACT WITH MULTI-STATE PRIVILEGE". Would it help my application if a apply for a RN license in a random compact state? Then start applying to the jobs that require a compact license?

I'm also applying to jobs within California. Can I have licenses in multiple states at one time?
In a word - YES. Your application will not be seriously considered unless you are 'good to go', especially since you are a new grad. It's even better if its associated with a local address if the organization is in an area that has a surplus of new grads. Best of luck on your job hunt.