Convert SE panel from two 100 amp breakers to a single 200 amp breaker
No, you definitely can't do that with this meter-main!  You have several choices.
Put only one panel on the ATS
This is the normal approach to this problem.  You pick one panel and make it the ATS-operated panel. Any critical loads in the other panel, you reroute them.
You can also put the other panel on a MTS (manually operated interlock) and those are $100-ish for most panels.
Two ATS's, one for each panel
This is also allowed though at higher cost and complexity, of course.
An ATS that stacks under the electric meter.
Some ATS's have a funny plate that fits between the meter pan and the meter, thus switching the entire service.  That type of ATS will work very well in this instance.
Replace the meter-main with something appropriate
Into the trash goes both the meter and the dual main breaker apparatus. Then you fit a meter-main designed to support an ATS, or a plain meter feeding the ATS which then feeds a 200A panel which has the two 100A breakers in it.