Yes. Once you are approved for life insurance and have paid your first month's premium, you have coverage "In Effect".
So, if you should pass away, there would be a death benefit paid out to the beneficiary of your life insurance policy, subject to the terms, conditions and exclusions stated in the insurance contract.
There are life insurance plans that allow you to apply online and find out if you qualify for coverage the same day.
These instant issue life insurance policies are usually "term life insurance" plans, which means you have temporary coverage lasting for a duration of up to 30 years, depending on the "term" of coverage you selected for your plan.
Learn more about life insurance that pays immediately.