No. In order for spouse/dependents to get 36 months of COBRA from the date of Medicare entitlement, the employee must be entitled (enrolled) to Medicare before the qualifying event (termination).
When the employee is entitled to Medicare prior to the qualifying event, the spouse and dependents are entitled to COBRA for the longer of:
(a) 36 months from the date of entitlement to Medicare Part A; or
(b) 18 months from the date of retirement.
For example, if the employee turned 65 more than 18 months before termination, the spouse and dependents will be eligible for COBRA for up to 18 months from the date of termination, because that's longer than 36 months from the date of Medicare entitlement. Whereas if the employee is enrolled in Medicare on August 1 and then terminates employment on August 31, the spouse & dependents are eligible for 36 months of COBRA from the date of Medicare entitlement (i.e., 36 months from 8/1). The employee however is only eligible for 18 months of COBRA.
See IRS Revenue Ruling 2004-22 (page 554)
