@ SABRE
Yes. An AIP supported SSK can function as a deterrent platform. This is the direct answer. But then so can a non-AIP SSK. To break the notion into smaller pieces: deterrence means a measure of assuring your enemy that you can hit him at least as serious as he can hit you. That you have the technology, will and delivery systems available to do that. To use a SSK in this context, sure why not? To expect to do it as efficiently as with a SSBN or a SSN/SSGN? No way.
AIPs are auxiliary systems helping a conventional sub to prolong its submerged operation. Days maybe a week. In your scenario, you mentioned a standoff between the two countries of months or even a year. No AIP will help your SSK to stand submerged for such a long time. You have to take into account that whatever sources your AIP is based on – whether is a close cycle engine or exotic fuel cells – these DO have a limited period of life, an expiration date if you will. It’s not like a nuclear reactor that needs refueling once in 25 years!
AIPs cannot assure a greater overall endurance OR power (at sea) than conventional (atmospheric) propulsion.
Also let us assume that the cruise missiles will have a range between 700 to 1000Km and thus may need to stay within or near the coast. How would the enemy's advance ASW system effect the SSK's deterrent role than?
An enemy with an advanced ASW capability – as you mentioned – can prosecute a slow submerged moving submarine in a very excruciating way. He can cover a far greater area than your SSK would be capable of at any period of time. Once he knows you’re there somewhere, he can place a quarantine zone of tens of thousands of meters around you and if he's not prosecuting you with warning depth charges, he can just wait for days on end for you to try and break the quarantine zone or – when your AIP is exhausted (meaning you begin to lose your life-support features – electricity, oxygen, heat, water etc., the very critical features a nuclear reactor can guarantee for years) – for you to surface. And you know that when the enemy succeeded to force you to surface the game is over.
I suggest you read on how US NAVY did exactly that with the Russian SSKs deployed during the Cuban missile crisis. Or how Russians did that to a US SSK (I forgot her name) in the Pacific off Kamtchatka in the ´60s (IIRC).
Now, all this assuming that hostilities didn't break out. 'Cose if they did, you wish you've sent a nuclear boat instead.
I hope I shed some light on the issue.