The best way is to measure. GEANT4 does not account rise time of scintillation.

That is very difficult if not practically impossible and one will have to measure to be sure in any case (remember the mantra for simulations: garbage in - garbage out always verify your results).

A couple of issues:

1)  Geant4 does not produce all ionization electrons due to a low energy  production cut. But one could argue that  very low energy electrons recombine. The question would be how low the production cut should be and if the ionization model is valid for those low electron energies in the final state.

2) Geant does not simulate the electronic response, this is something you have to model by your self.

Actually Geant4 has the capability to transport scintillation photons and that could be used to get a time of arrival distribution at device which converts the photons to an electrical signal (Photo Multiplier Tube, Photo diode ...). But the electronics PMT/PD and (shaping) amplifier are also and often more important factors in determining the rise time which are not simulated by Geant4.

The best way to do an a'priory estimate is to read attentively existing books on a passage of charged particles through a medium. Geant4 (later on there will be Geant 5, 6, 7, ..12 and a completely new package written on a language which is not invented yet!) is not a "guru"!.

If you would know how ions travel in a gas and what are relevant parameters (like E/p), which were discovered in Fano's time (do you know, who is Fano, where he works  and what is the "Fano factor"?) , then you had haven no problems with answering your question.

Nobody from the net will do your work for you, sorry!

If you are scientist, look at the essence of things, not on the current instruments, how to get an immediate answer for your superviser!

I appreciate all of the efforts.

we can use G4timer