In principle, yes. That is why you need to check with any flying school how they charge the time because time invoiced is not necessarily time logged. Plus, there is the anomaly between LASORS and the ANO!
As with so many things, have a chat with your instructor.
However, I am struggling to believe that an R44 PPL would be cheaper than R22 even allowing for datcon readings. An R44 is about 50% more per hour than an R22 so I don't think you'd be saving.
Cheers
Whirls