You cannot use the full function because it is foundamentally a logaritmic function. For the ADC convertion you need a linear function. Once time, resistence and capacity are fixed than the charging function depend only from the voltage applied. If during the charging time you do not pass the 1T point of the function, than the charging function can be considered "quasi liner" and the system work. In other words you can deduce the value of the voltage applied. If you pass the 1T point then thing become more complicated since from that point on the function is purely logaritmic.

Cheers
Al.