How does the nRF24L01+ performance degrade with supply voltage?
This doesn't seem to be spelled out explicitly in the datasheet but there are a few hints at it. Apart from the lack of an external inductor or capacitors for a boost regulator (which I'd expect even though technically they could be on chip) there is the following description of VDD_PA:


  Power Supply Output(+1.8V) for the internal nRF24L01 Power Amplifier. Must be connected to ANT1 and ANT2 as shown in Figure 30.


So the RF power amplifier is regulated down to 1.8 V so I wouldn't expect power output to vary as the voltage drops towards the lower operating limit. For the receiver sensitivity there's no mention of it being measured at a particular Vcc level and I'd expect internally that's because everything is running from the output of a 1.8V linear regulator.

Apart from obvious current draw measurements about thing I can see that makes mention of different operation versus operating voltage is on page 13 of the datasheet related to the maximum digital input voltages, but no doubt that would just be related to clamp diodes attached to the external Vcc.

There might be some reasons for slight changes in performance, such as internal heating or lack of it. But I'd expect any differences to be very small compared to external factors so I think as long as you stay above the specified 1.9 V minimum with a small margin for any noise on your supply the idea is sound.