It is exceedingly rare for coverage to be continued after the termination of an employee, because of on-going treatment. I'm not saying it never happens, but it is unusual enough that IF your wife's plan were one that provided that, it would say so in the plan booklet. If the plan is silent on the subject, you can pretty much take it to the bank that no such extended coverage exists.
If you sign up for COBRA, the COBRA coverage MUST be retroactive to the date of cancellation so that insurance coverage is on-going. It is legal for them to cancel the coverage until such time as they receive her signed COBRA form and her first payment, but at that time they MUST make it retroactive so that there is no break in coverage. There are no circumstances whatsoever in which they can start COBRA coverage on any other date except for the first date of cancellation.
So once she has signed up for COBRA, the specialist visit would be covered just like any other visit.