No.
Generally you will be transferred every 3 years. This may extend to 5 years also. The department is not as lenient as many other departments in matters of transfers and postings. The headquarters usually transfer you once your time is up.
In fact, one of our directors, opted to be transferred early because his son’s 10th standard would coincide with the third year of his posting in Shimla. If you are someone who would not like to ring bells for being posted in the same place, then you might not be happy with the transfer policy in IA&AS.
That said, there are exceptions to this also. There are instances of officers who have served in their home state for more than 10 years. You can also opt to go out for 2–3 years and return to your home state. Another option, if you are not from North East, is to ask for a posting there, after which usually choice posting is given.