If you are married in a community property state, there will be a separate clause on the beneficiary designation form where the spouse has to sign in order to waive their rights to the benefits if they are not designating to their spouse.
If the spouse hasn't legally waived their rights to the benefits in a community property state, then they can claim part of the life insurance payout, and the company will just give the remainder of the benefit to whomever the person designated on the form.
I'm not exactly clear on what you mean by paying from "separate property" as money is rarely ever considered separate without a prenuptial agreement involved (especially so in a community property state), but I doubt the method of payment would be considered. It would be hard to prove that none of the premiums were paid by joint funds and would be far easier to just have the spouse waive their rights to the insurance policy if they planned to pay for it with separated funds.