As far as I know, everyone has to undergo medical exams for the Spousal application. (Unless Americans are exempt of that).
Your application is very new, and the background in progress you are referring might have not started yet. (Depending where you are checking). Are you checking that information on the tracker, and if so which tracker, yours (PA UCI) or his (Sponsor UCI)?
For inland applications the estimate time is 10 months, but some of them do get their application earlier, I believe the earliest I saw for inland was 5 months.
With the AOR you received, you can get a OWP.
No one can say which one will be done first, so in that case my suggestion would be to apply for an OWP asap and whichever comes first, great!