yes totally. There is a great DIY project for doing that https://www.fourmilab.ch/hotbits/
It's not required to have the particle energy measured for making random numbers, detecting precisely the arrival time of particles is more important plus having a high hit rate is usually desired. My DIY detectors are not optimized in that way but it would work in principle. Timestamps are already recorded by the python scripts on github, it would be just a matter of evaluating them.