You're somehow mixing Acquisition time with the linearity of the ADC conversion function.

For the Acquisition time, you need the sample cap to charge to whatever value you want the ADC to convert. Period.

The time constant of an RC network is T=RC, and after one T the voltage across the cap is roughly 66% of the input voltage.
If you look at T vs percent, you get:
Code:
1    63.2% 
2    86.5% 
3    95.0% 
4    98.2% 
5    99.3% 
10   99.995%
20   99.9999998%
If you set the Acquisition time to 1T and then convert the value, you could be VERY wrong... 37% wrong. Of course, that depends on the new input voltage you want to convert and any existing charge on the sample cap, but T gives you a worst-case number.

For example, an 8-bit ADC (1 part in 256, or 0.39%) would need an acquisition time of better than 5T, but there's nothing wrong with giving it 10T or 20T or 100T, as long as nothing else changes in that time.

You do not have to hit some magic 1T window trying to get it into a "quasi-linear" range, or guess at things to "see if it's good enough".