Does the power up timer make it so slower-than-specifications Vdd rise rate is allowed?
No, non-linear Vdd rise and slow (out of specification). Vdd rise are not fixed by using the power-up timer. The device rise rate specifications on Vdd always apply.
The power-up timer helps in situations after the internal device BOR is released (e.g., if there are small disturbances on the supply voltage after the BOR release). On devices with configurable power-up timers, setting the power-up timer to a long delay (128 ms for example) willnot allow the device to have a 120 ms Vdd rise for POR and operate successfully.
Another example of a case where a power-up timer does not help is when there is a voltage difference greater than 300 mV between Vdd and AVdd during Vdd rise. Meeting device specifications are of primary importance.