Yes, it is possible but not straightforward. Assuming your AICC compliant LMS supports HACP, you can link to external AICC content. That's the easy part. The problem is that the Moodle quiz is not designed to support AICC, so you need a sort of adapter that talks the AICC talk and can listen to the quiz and communicate with the LMS as required. That's not too difficult.
The other challenge, if you want the user to be signed on and granted access to the Moodle course and quiz on launch, is SSO. The adapter will have to take care of that. One (proven) approach is to build on Moodle's ability to be an LTI provider (requires the local_ltiprovider plugin or equivalent) and let the adapter translate the AICC launch request to an LTI launch request where the target quiz is set as an LTI tool.
I know that's very brief but hope it helps nonetheless.