No, you have to shop your own policy asap!!!!

usually retail policy is cheaper than Cobra.  but it takes time (more than 2 wks) for insurance company to approve your application.  most importantly, once you past 63 days gap, you may get denied by insurance company for so called "pre-existing condition".  

so, the key is 63 days.

also, make sure policy covers local service.  e.g. Kaiser is not available to most states.