As per the Cat Fanciers’ Association (CFA) breed standard the eye colour of the Siamese cat is always a “deep vivid blue” and that eye colour is the same across all the different Siamese cat colours from seal point through to chocolate point, blue point and lilac point. And it is the same across the cat associations. For example, The International Cat Association (TICA) ‘s breed standard refers to Siamese cat eye color thus: SI/BA – Blue. ‘SI’ means Siamese and ‘BA’ means Balinese (longhaired Siamese).
The answer to the question in the title is a very confident NO. Siamese cats cannot have green eyes. You might see some Siamese cats which are not true, purebred Siamese cats with green eyes but they cannot be formally described as a true Siamese cat in the West.
And that statement is reinforced by the list of reasons for disqualification of a Siamese cat from a cat show competition. One of those reasons is “Eyes other than blue”.
The irises of the eyes of Siamese cats contain only traces of tiny pigment particles. These are particles of melanin. And because there is so little melanin in their eyes due to the cat’s genetics which create the Siamese cat coat, it is the white light which is refracted through the eye which makes them appear blue.
To put it another way, the Siamese cat’s eyes should be a vivid blue and that blue is not caused by blue pigment in the iris of the eyes but the reason stated above. I think that you’ll find many Siamese cats have an eye colour that is not exactly vivid blue because refracted white light doesn’t normally created a vivid colour (please leave a comment if you disagree).
And the reason why when white light is refracted you see blue light is the same reason why the sky is blue. Below is an explanation according to NASA.
Blue light is scattered in all directions by the tiny molecules of air in Earth’s atmosphere. Blue is scattered more than other colors because it travels as shorter, smaller waves.
That is pretty much all you need to know about the Siamese cat in response to the question in the title.