You _may_ be able to determine the number of radioactivity events (becquerels). But you will not be able to determine the type, or the strength of the radiation. So you will not be able to measure rem.
On the contrary, like one of the comments on that page says, you are likely to only detect gamma. Alpha and beta will be stopped long before getting to the sensor.
Not all gamma is the same, the energy matters a lot in terms of how it affects the body. And of course when calculating the dose you need to know the energy - you add the total energy, not the total number of photons.
Alpha and beta from distant sources will be blocked of course, but if there are radioactive isotopes in the environment they may decay right near the sensor, and you won't be able to tell.
Distant gamma is a much smaller concern than radioactive isotopes in the immediate environment.
True about the gamma energy dependence, of course, but alpha and beta won't really get to the sensor unless the decay is inside the camera. And even gamma doesn't have that long range, even in air. You pretty much have to have contamination nearby.
For reference, you can comfortably detect, measure and map ground produced gamma radiation from natural elements from a distance of 50 - 80 metres in the air above.
There's also a respectable number of cosmic ray events in the atmosphere all the way down to ground level leading to high energy gamma counts as a matter of course.
Radioactive Iodine and Ceasium particles (in small numbers admittedly) made their way across the Pacific and became gamma emitters caught up in the air scrubbers of the University of Washington in Seattle.
Well, cosmic rays can have energies far, far higher than you get from typical radioactive decay, so they (or gammas produced by them when they hit the atmosphere) have a lot more penetration.
And rem is what matters for most purposes.