I'm not sure. The ammo types a weapon can use are defined in the actual weapon block itself, so unless WeaponCore does some scripting trickery to pull the original block's ammo data, it will likely need a patch.
Keep in mind that Scarce Resources no longer entirely removes magnesium from everywhere but Triton, but it now exists on Earthlike in desert boulders.

Hi, I've been using Scarce Resources for a little while as I like the incentive to explore the other planets, but I also enjoy using many MES mods, Because of how rare magnesium is it's very difficult to defend myself early on, so I was thinking of using this mod. I also use weaponcore, and I was wondering if the new ammunition that your mod adds would even work at all with the weapons from weaponcore. Thanks for the cool mods!

Those are exactly the ratios in Scarce Resources.
They're roughly replicated here, replaced with Low-Grade Magnesium.

A future plan for this might be re-adding the actual ore deposits, replaced with Low-Grade, leaving Triton with the pure stuff.

I have been considering an expansion of this concept to other ores, creating Low-Grade versions of them for planets not considered their primary, and having the ore produce a lower amount of the product along with some gravel to make things more complicated and further encourage getting the high quality ores.
Of course, I'd leave other ores as purely exclusive to certain planets, but I do like the idea of, for example:
High-Quality Gold primarily on Earthlike's moon
High-Quality Silver on one of the other moons while the others keep the low-grade stuff
Low-Quality iron in asteroids or something.
Would allow us to expand the resource distribution without having to make more exclusives.

As far as I know, Mg still spawns on Earthlike planets on surface rocks, just with a low chance. 32%-12% Desert - Forest Biomes and 0% in snow biome. Does the Low grade Mg spawn more frequently in your surface rocks?