"Q will essentially be applying for a graduate visa"
Not just "essentially" but that is the only visa that he can currently apply for. As long as his student visa has not already expired then he can take up his position as an MSP
"The graduate visa will be approved"
I agree, it most likely will be.
"...and Q will have 3 years to accumulate the experience and time towards applying for skilled worker visa and then, later, ILR."
Yes, he will be able to remain in the UK for three years with a graduate visa. But what happens after that?
Being an MSP is not a job. An MSP is an "office holder", not an employee. It is specifically excluded from the skilled worker visa:
https://www.gov.uk/government/publications/skilled-worker-visa-eligible-occupations/skilled-worker-visa-eligible-occupations-and-codes
So, the skilled worker visa is out (this is why it has been reported that he is not seeking to apply for this). What about the global talent visa?
This visa is strictly limited to people who are leaders, or potential leaders, in specific fields.
Applicants must be endorsed by one of six designated bodies that assess expertise in specific fields. These are:
Arts Council England: architecture, fashion, film, TV etc
Tech Nation: digital technology, software development etc
The Royal Society: natural sciences and medicine
The Royal Academy of Engineering: engineering
The British Academy: humanities and social sciences
UK Research & Innovation (UKRI): academic science and research roles.
.
You will notice that neither the Scottish government nor the Scottish Greens are included in that list. There is no endorsing body for politics or elected office under this route.
OK, so you might suggest that he takes up another part-time job as well as being an MSP so that he might qualify for a global talent visa. The trouble is that the Scottish Greens have a ban on their MSPs having other jobs.
.
So, once his graduate visa expires after three years then he is out of the country half way through his term.
What are the Greens going to do after that?