The most recent Android build for the MC3200 series is still Jellybean (4.1.1) and unless you can see the Play Store icon in the launcher, it does not have Google Services.
As you have already figured out, it is not immediately obvious if that version supports TLS 1.2. I don't have a 3200 available to verify it myself so my suggestion would be to attempt to enable 1.2 manually in your socket factory.
There's an example of doing just that at https://github.com/square/okhttp/issues/2372 , adapting it to client library other than OkHttp should be straightforward. This method is a relatively quick way to validate whether TLS 1.2 is available on the MC 3200.
Make sure to perform the test on the same version of the OS your customer will be running or, alterntively, run it on the latest one and make sure your customer will be upgrading their devices to it. You can find the different releases at MC3200 Operating System for Android SKUs Support & Downloads | Zebra
Technical Architect, Kutir Mobility
Posted on behalf of Zebra Technologies
Oh, sorry I should mention this before but I haven't got MC3200 either. Now app works on Android 7.0 device, where we haven't such problem.
The customer only wants to use MC3200 and asks is it possible or not.