The TL;DR answer: Not possible.
The long answer:
The F1 allows you to set several different modes in the NI Controller Editor for the pad LEDs; 1 colour, 2 colour, HSB (Hue, Saturation, Brightness), and Indexed.
The 1 and 2 colour options are pre-determined in the Controller Editor, so any MIDI signal on that button's channel / CC will either say "Make the LED bright! / Make the LED dim!" or "Make the LED colour A! / Make the LED colour B!", but HSB and Indexed receive additional signal over MIDI to specify additional information. Unfortunately there isn't much information about Indexed colour mode on the NI website (or even trolling a few support forums), but HSB is super functional... if you can map it all out, which unfortunately you can't do within rekordbox, and here's why...
My F1 was defaulting to send/receive signal on MIDI CH13. The first pad, top left, was sending / receiving CC10 (BC0A) when pressed (or to send the standard "light up the LED"), the values toggle between 0 and 127 for those functions, pretty straight-forward.
But if you enable HSB mode for that pad, you now have to send 3 additional MIDI signals to the LED on CC10 depending on what colour you want, and how bright.
MIDI CH1 sends hue (the colour), MIDI CH2 sends the saturation (0 being none; white, 127 being full), and MIDI CH3 sends the brightness (0 being "off", 127 being full on). So in the software (whatever software) you have to specify that you're sending up to 3 additional MIDI signals to the controller. Realistically, you don't need to send the saturation item as you'll likely want it full value. The brightness would be your on/off, which only needs to be sent if you have a hot cue. The problem is then what value (colour) is being sent from the software to tell the pad to be the same colour as selected for the hot cue ... there is no ability to draw that dynamically from the software to send to the MIDI pad LED.
I would assume the NEON or other RGB-capable controllers work in a similar fashion, more likely indexed (the HSB mode is pretty advanced and cool to see available), but as the Pioneer DJ controllers are using HID and MIDI mode, they have a better integration for the LED output colour data from the software.