Muscle plasticity is not the same thing as regeneration.
Muscle plasticity is defined as the ability of a given muscle to alter
its structural and functional properties in accordance with the
environmental conditions imposed on it....
From birth until death, skeletal muscle is in a constant state of
remodeling in order to adjust to changes in load, activity, or
innervation. This unique plasticity allows muscle to alter its
structural and functional properties in accordance with its imposed
environmental conditions. This is widely recognized in sports, where
muscle changes imposed by training in athletes leads to obvious
phenotypic modifications that optimize the specific performance of the
muscle. The number of muscular contractions (activity) and the degree
of loading appear to be the dominant stimuli for training-imposed
muscle changes. For example, body builders perform low frequency, high
load contractions that result in muscle growth (i.e., hypertrophy) and
an increase in force-generating capacity. On the other hand, marathon
runners perform high frequency, low load contractions that are not
associated with hypertrophy, but cause muscle fibers to assume a more
fatigue-resistant phenotype. Although genetic pre-disposition is also
important, these adaptations, substantially contribute to the
different physical attributes of body builders and marathon runners. (ref)
Exercise does break down muscle fibers. When you sleep, your pituitary releases growth hormone which helps in rebuilding the muscle to be stronger. The exercise doesn't build the muscle directly, though of course it's the catalyst.
After you workout, your body repairs or replaces damaged muscle fibers
through a cellular process where it fuses muscle fibers together to
form new muscle protein strands or myofibrils. These repaired
myofibrils increase in thickness and number to create muscle
hypertrophy (growth). Muscle growth occurs whenever the rate of
muscle protein synthesis is greater than the rate of muscle protein
breakdown. This adaption, however, does not happen while you actually
lift the weights. Instead, it occurs while you rest. (ref)
While you might call this normal nightly rebuilding (something that happens every night, regardless of activity, if you have enough growth hormone) regeneration, it's not the magic regenerative serum you reference in healing injury. I'll note that you refer to "wear and tear" but your examples are about injury.
When you tear a muscle, you literally tear it. I've had hard workouts that have left me sore for a couple of days. But one day (literally in a fraction of a second) I tore my calf muscle. It wasn't even that bad a tear (level 2 out of 4), but I was on crutches for 2 months.
When you tear a muscle or break a bone, you can not put weight on it while it's healing. And healing takes time. It was 2 weeks before I was allowed to put any weight on my leg and another 2 weeks before I could gently walk with most of my weight held up by the crutches. Broken bones take longer. (Where the break or rip is will change the timing, but it doesn't change the reality of healing.)
If you want to use magic for this overnight healing, sure, go ahead. Or if you want to call it science fiction and handwave how it works, okay, it's your story. But you're asking for science-based and the science simply isn't there. Might it be in the future? Perhaps to some degree. But only in that it will speed healing, not make it unnecessary.
When your soldiers train while they are injured (this is implied by your wording, even if it's only for a couple of hours, it counts), they are compounding the injury many times over. Training hard again the next day would compound the original injury as well.
My frame challenge to you is in how you incorporate the idea of outright injury into this program. That's not how you make soldiers stronger faster (or ever). Perhaps you didn't mean to put it that way, but I can only answer the question in front of me, not the one that's actually in your head.