Ok, just verified in a little break at home, you can play the one chosen synth or sample program / track when you're in Song or HD Record mode.
But like I said you're limited to that one track you have chosen before going into Song/HD mode (from the 5K itself or a fixed channel external controller). No way to change the active track or program parameters from within Song/HD mode from the UI.
I haven't tried with different Midi channels assigned to different tracks that are mutitimbrally controlled from one (changing channels) or more external Midi sources.
In my setup the 5K isn't set to be multitimbral, I'm recording on active track after track.
Maybe it's possible if it's set to Multi, but I would use seperate Midi controllers in a live scenario, since changing the channel while holding a key/note will certainly cause the previous note to sustain an cause havoc. No Midi Panic button, only 3 x stop and you know what that does

The most limiting thing would be that the patch parameters can't be accessed from the 5K menu itself in Song/HD record mode. Maybe you can program an external controller to send the according Midi CC messages to control synth/sample parameters.