Unfortunately not. At ParkBee you always need a mobile phone with the Parkmobile or Park-line app and (shortly) a mobile internet connection. To start and stop the parking action, internet is required but during the parking action the internet can be turned off (you still legally pay for your parking time).
But Parkmobile/Park-line have the possibility of checking in/out by text or phone. This is true, but this is not available for ParkBee locations since you have to open a barrier as well, and this doesn't work with that function.