How to sense the two magnet attracting each other
If I understand your setup correctly, then yes, it should be possible to detect this with a magnetometer. If you stick two magnets together, they behave (in the first approximation) as one larger magnet1, so the field should increase. For larger flat magnet and near its center, it should almost double, at least theoretically. You can test it in this simulator for example.



But in practice there is typically lot of unwanted and unexpected effects when doing any measurement, so the best is to try it experimentally in your particular setup. Get some magnetometer, which 
has enough range for field intensity close to the surface of you magnetic sheets, attach it to the middle of one sheet (with some small non-magnetic material spacer maybe), measure the field, put other sheet in place and measure again. You should, hopefully, see significant and reproducible change in the measured value.

I think this question is quite interesting and it would be great if you can share your findings in case you actually do such experiment.