So whatever the answer to your question may be, it really doesn't matter!
If it doesn't matter than everyone from Sera, Drepung and Gaden who has studied may call themselves a Geshe and forget the exams. If he was awarded the Geshe before the exams changed, then he is still a Geshe. But if he has never taken the exam before or after the examination systems changed, then he is not titled a Geshe?
A doctor of 60 years ago would not be able to pass the examinations of a exam for today's doctor. But he is still a doctor as he passed the exam of 60 years ago.
Ok. I'll take the bait one last time.
If a student is absent for an examination, they are often granted a degree on the basis of their attainments so far and the opinion of the tutors.
On the same basis, if someone is recognised by HHDL and his root guru as a Geshe and an excellent Spiritual Guide, then I'll take their word for it, as they know the level of his attainments.
Or was the Dalai Lama incapable of that judgement, and Trijang Rinpoche also ? Other Geshes also received the title without taking the final exam, such as Lama Thubten Yeshe, founder of the FPMT, or so I have read.
Look at it from the other end of the telescope:
Since it is obviously the case that someone called a Geshe in the Gelugpa tradition need not to have taken all the exams but can be identified as such by his gurus, then it is obvious also that the answer to your question is logically 'Yes, GKG is a Geshe'.
Those who wish to claim that GKG is not a Geshe are therefore also saying that HHDL, Chenrezig, is capable of being wrong on a really basic issue, and that Trijang Rinpoche is also wrong. This would be unthinkable to the Tibetans who view HHDL as some sort of God King.
In the UK we can call ourselves by any religious title we like, simply by changing our name. To do so in order to deceive would be very wrong, but the case of GKG is very well documented and any hint at deception easily refuted, as it has been many times.
For all the above reasons, to me it does not matter at all. I can't of course speak for those who may be desperate to smear GKG, and cling to any view which feeds their anger - which is very sad.
To the NKT in moving forwards, this issue is long dead, but I do wonder why it keeps being dredged up. If it could somehow be proven that he was not a Geshe, as there is no longer a connection with HHDL or the Gelugpas under his rule, it does not matter.
The NKT has flourished worldwide, bringing the Dharma to many thousands of students, many of whom can attest to the efficacy of the teachings, so why would it trouble anyone what title was given to the head in addition to the crucial one of Spiritual Director of the NKT, which he has now passed on to his successor?
For all the above reasons, I say again - it does not matter.
Well, as a personal view, interesting as it is to dig up old smears which may also be slanders, I for one am happy that GKG is a Geshe.
We would spend our time more profitably, perhaps, in examining the current actions of those who also hold the Geshe title, a status which has made no difference in their support of violent oppression. For their actions and their breaches of samaya, perhaps we should consider whether they should immediately disrobe, let alone fuss about their Geshe degree.