It would totally be gravy.
I've actually started that type of conditioning work and while my strength hasn't gone up, it certainly hasn't gone down. My breath and heart are a lot more conditioned it seems like. That is, I don't run out of steam as easily doing anything in or out of the gym. So when I do my main work, I don't need as much rest over time. I've noticed that my all of my muscles seem to like to grow from this type of work. My best guess is that my muscles happen to do best when exposed to a high amount of time under tension. Granted, that is just an educated guess at best.
I typically do 4-6 sets of tire flipping, some type of carry, sled pushing/dragging, seated sled dragging which means using only my upper body, sled upper body pushing, short jumps or KB swings, med ball slams, different kinds of med ball tosses ,rope work, jump roping, bodyweight circuits, or any combo for about 45s-90s at a time with 2-3 minutes of rest in between. I'm working on adding more and more sets. I started at 3. Pretty much, I do what I feel like and know that I'm doing it right when I feel a little nauseated and lightheaded by the end. Allegedly, I've heard that's the lactic acid and growth hormone at work! That kind of work to rest ratio falls into what's known as anaerobic lactate training if you want a fancy name to peg to it.
Just understand that you may not make strength gains as easily if you prioritize this. But it's totally okay to put one trait on the back burner to focus on another. Even specialists like powerlifters will often emphasize a trait like conditioning over other work far out from a competition.
Granted, when you add one thing you often have to take away from another. Granted, if you work at it you can gradually add your work capacity over time.