First, welcome to the forum - glad you found us and hope you find what you need and also contribute some. To your query - I think it will, although a third-party installer and the dealer is much better equipped to answer. If the product were Audi parts and installed per their instructions, you prolly would be fine. But since I know of no such kit or parts for it on the Q3, I suspect you'd violate at least Audi's rules to safely operate and that might likely incur a flag to void some parts of your warranty, perhaps not all, but several... Just my opinion.
My local dealer told me that the Audi electrical system (like most/all European vehicles, he said) are built on a low-voltage system, and a remote start system cannot "safely" function in that environment, and added that installing one after-market would likely void my warranty.