What is your question? Can you clarify?
If you are asking if an always on implementation can support a SQL Managed Instance, then the answer is yes.
As for a "distributed query", are you referring to a cross database query? If so, the answer is yes.
If you are talking about 'Distributed transactions", the answer is also yes
https://learn.microsoft.com/en-us/azure/azure-sql/database/elastic-transactions-overview?view=azuresql