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Does the above impact Microsoft AX2009?
Is your AX already installed? Maybe you can get problems with Reporting and Analysis Services.
I don't think you can downgrade major versions (like 2012 to 2008) of SQL Server in-place. You might be able to downgrade Editions (like Enterprise to Standard).
As for AX2009, the only thing you need to make sure is that the database is accessible by the AOS service.
U can create SQL script to perform same. Right click on DB > Task > Generate Script > Run Wizard. This will generate a script. Run the same script to the SQL where u want to migrate to..
Just make sure network is same, as data will have domain and SID info stored. Also, both old & new DB server should be able to talk to each other.
Also u can follow this article