Buck/Boost converter interaction with MCU in sleep mode?
The front page of the datasheet shows operation down to light load; 80% at 100 uA load. Although the 2 A output seems excessive for a remote, this device is a reasonable choice. If TI has one that has a lower maximum output current, you will gain a little more efficiency at low loads because the gate charge in the power MOSFETs will be lower. Gate charge is all loss.

From page 16 (typos are TIs):


  8.4.2 Power Save Mode Operation
  
  Besides Continuos Conduction (PWM) Mode, TPS63802 features Power Safe
  (PFM) Mode operation to achieve high efficiency at light load
  currents. This is implented by pausing the switching operation
  depending on the load current.


This means at light load there will be ripple on the output. The converter will run for a few cycles and bring the output voltage up. The converter tuns off and the load (your uC in sleep state) draws the output back down. Page 17 of the datasheet has a drawing of this.

The TPS63802 will still draw current to run its circuitry. The datasheet quotes 11 uA.