My question is [ : is it indicated that ] the conditioning/GPP that complexes provides means that I do not need to do cardio?
Forgive the edit. I had to reread it a couple times to think about the way you're posing the question.
So, my understanding of the question is that you're wondering whether the burpees and jump rope practice substitutes for unspecified cardio training.
The answer is either No or yes depending on how you mean it.
Endurance or strength endurance ?
The thing is that I draw distinctions between burpees and running. I don't regard burpees as a cardio event. I regard them as a strength endurance event; A question of how many times can I use strength to exert this dose of force. That's a different thing for me than running or jogging or bicycling. Burpees are pulsed discreetly like pushups. Another strength endurance event. This grants the motions primary access to atp/cp exposure at first and digs into glycolysis second.
In bicycling thinking how long can I generate continuous motion forward with the benefit of momentum and the consequences of lost inertia over terrain. And a bicycle machine pedaled at a maintenance pace can be characterized as primarily aerobic fatty acid metabolism followed by glycolysis and in rarer events primarily CP fueled, momentarily.
Stress and recovery
I've been puzzling over this in reading and looking at
@Brett Jones iron cardio routines. I fancy them to be strength endurance events.
And I've been fascinated by the differences between breath recovery and heart rate recovery.
I note that in my clean and jerk practice my breath recovers without fail every 30 seconds. While my heart rate is mostly steadily rising. It dips a little but not much.
Conditioning masquerades as cardio
There is some conditioning aspect that's improved by such a practice but on its own it hasn't expanded the distance, nor increased the pace at which, I can walk jog or run.
Also cardio events are exquisitely discreet, preparation wise. That is to say bicycling will do little to prepare you for a foot race and vice versa. And , I harken back to an old study where they had participants practice on a one legged bicycle with only one pedal. And they measured improvements in the vo2 max of the participants in the study. Then after a time , the switched the side of the pedal and it's as if they never rode the bike at all. All those gains in vo2 max were "lost".
All that to say that in my day to day life I can get away with substituting my cardio with some conditioning. Seems to work well enough. I can carry more and heavier boxes from the car, and it's easier to get up and down the stairs and I can pick up the kids and hold them for a while longer. But if you have a goal to run further, and faster, you're not gonna get significant improvements from anything other than training for your running directly by running.