Oh yeah it definitely will. Just like boots you're gonna find a brand that really fits like a glove, so if you can get to a good store with a shit-load of brands you might be pleasantly surprised. But you really need to run in them to really see what's what. That's why a store with a treadmill is so important. Some brands are made to feel oh so cushy when you first put them on, and that can be deceiving. You need to see what dynamic feel is like. Don't get me wrong, it's a good start, but when you're in motion you might feel a difference.
You might have noticed that lots of folks wear sneakers every day just for the cushioning. So a nice soft ride is great if you're just stroking around town. But the real specialty running shoes come alive when you're laying it down.
On inserts, I don't want to steer you wrong, sometimes they're definitely needed, but I think lots of times we over-correct these things. I wore them for years myself, but slowly worked my way off them. I now run in a completely neutral, mid-drop shoe, and do just fine. But I worked up to that point, where my feets where strong enough for it.
And speaking of that, a low drop shoe is normally a neutral shoe; putting an insert in it is creating a stability category shoe. Which is fine, but you can do that with several other brands, by themselves. Try a good light stability shoe without an insert, on a treadmill, and compare to what you're doing now.
There may also be other issues at play; I am guessing that you might be a spartan-sized warrior, if you prefer a heel strike. I find the heavier I am, when doing ruck runs, the more I go back to heel strike. But when race weight, I can and will move up to mid-foot strike. On longer races I will even alternate and give different muscle groups a break.
One technique I use is to do some heavy 5 x 5's, with some squats, leg presses, extensions, etc. Then I go out and do a 5-10K run. This will really help to strengthen those quads, and teach them to run when really fatigued. So you can stay on your fore foot longer. Think of it this way. Heel strike is on skeletal system, fore foot is using arch of foot as leaf spring, and quads as shock absorbers. Ideally that's where you want to be (in a nice neutral, low drop shoe), but cushioning will allow you to heel strike, if that's where you need to be. (And actually Hokas do both, so that's why I use them).