Incorporating military training when bulking?

Is it possible to incorporate extreme cardio activity when bulking if you're still in a caloric surplus?

I'm planning on wearing a bergen or backpack with around 25kg. Then walking for long distances (miles) under a specific time parameter. Then I will focus on completing the route in a quicker time, pushing my limits to train myself mentally & physically.

How would military training effect muscle building if you are still eating above maintenance?
Specifically British Army training regime, if anybody has any first-hand experience in the military.

Also, what benefits bodybuilding wise could I expect to see from military training? Would my compound lifts increase/decrease?

I'm not familiar with British Army training, so take my experience with a grain of salt.

I regularly incorporate rucking into my training program. Usually 40-90lbs (18kg-40kg approx) for 2-6 miles. Never really gone longer than that, and while I tend to try and monitor pace over shorter rucks, longer rucks tend to be incorporated with hiking in the hills and that tends to make pacing pretty difficult at best, and virtually impossible on steep climbs or in mud. In those cases I just do my best and keep moving.

I did not find that I lost any strength, but I wouldn't say I gained any either. This tends to be pretty low impact, but it will wear out your traps and I always wound up with pretty tired glutes (again, worse on hikes where I was climbing a lot). I did feel like I recovered pretty well from these. Much better than recovering from a run of equal distance at least. In terms of cardio exertion, I found rucking to be every bit as challenging as running.

In terms of how to mash this up with bodybuilding, I think the two goals are a bit at odds to get really good at either of them. I don't mind being a mediocre rucker (though I did complete a 10.5 hour event wearining my ruck with 20k), and I don't really care about six pack abs or giant biceps, so it never bothered me that I wasn't maximizing my training towards one goal. For true military aspirations, I would strongly recommend forgetting bodybuilding type training. At a minimum dial back your expectations about what can be accomplished by quite a bit.

ruck marches are pretty low, unless you are pushing it hard, however you have to also keep in mind that in the military a bigger person is a much easier target. Which is why you're not going to see people built like Ronnie Coleman...but these same skinny people can put you on their back and carry you literally out of a hot area.

Since you are enlisting I would recommend you just get used to doing the PT that you're going to have to be doing. You can always hit the weights after you get through boot camp.