Would it break the suspension of disbelief to have the “most effective military by an immense margin” in the world (it’s basically the world police) be have only around 500 active fighters because they’re the only people highly trained to use magic effectively?
It will depend on your world building, but breaking suspension of disbelief is a real risk. Having only one military superpower in a world does some weird things. So, let’s talk international politics.
If your setting has multiple, viable, nation states, and one of them has an inordinate advantage, what you have is a monopolar system. Everything relates directly to that nexus state. Any interstate conflict will need to be measured, carefully, against riling the superpower, and any interactions need to be measured with consideration for their interests.
For example: If two if your states are negotiating a trade agreement, both sides are going to be concerned with how their treaty will affect their relationship with the nexus state.
If two states go to war, the presence of the nexus state’s interests will be a pervasive, and vital, strategic consideration. For example: If the nexus state citizen owns a mine in the disputed territory, the warring states are both going to need to be aware of it, and careful not to interfere with that holding’s ability to function.
How all of this will manifest depends heavily on how the nexus state works, and how presents itself.
Real world international politics is based off hard power, and soft power. Hard power is military capacity. (Technically, hard power is the capacity to coerce or force other nations to do what you tell them.) For your purposes, your nexus state has unlimited hard power. That is, kind of, how military superpowers work. (Though the actual math tends to be a little more sophisticated than this, because applying hard power usually comes with a cost in attrition.)
You can think of soft power as an “influence currency.” It’s the ability to go to another nation’s government, ask for something, and get what you want. Hard power can affect soft power (both positively and negatively), but there’s nothing inherently nefarious about soft power. It’s not coercive.
The interesting thing here is, while your nexus state has unlimited hard power, the other states can cultivate power in their interactions with one another. So, there is room for political maneuvering between them.
How your nexus state chooses to express their power will seriously affect your setting. If they’ve set themselves up as guardians of the world from all external threats, then they may be relatively hands-off. Individual states aren’t going to pick a fight with them, but they may feel free to squabble with one another. If your nexus state is involving itself in ruling the world, and views the various other nations as extensions of itself (as an imperial power), then those interstate conflicts are going to be mostly fought through political means, and may only engage in actual violence through proxies.
There is an interesting detail here that I’ve skimmed over, because it doesn’t apply in the real world, but might be a factor in yours. The rarer magical talent is, the easier it will be for your nexus state to maintain control over it. If your state has unlimited hard power, they may be able to parlay that into the ability to simply take any prospective mages from other nations. This would encourage the situation you’re describing. They control the only 500 mages in the world, and as a result, have complete power over magic. (You might be able to make a nuclear proliferation allegory out of this, depending on the specific scenario you’re working with.)
However, if they’re taking mages from the other nations, that would breed resentment. It’s possible those states might seek to keep some of their potential mages, hiding them, and training them in secret. Their training might not be as good, but if your mages are powerful enough to completely warp the balance of power, one or two could be incredibly destructive forces, giving a state some covert options that, “break the rules,” for how the world is supposed to work.
It’s also possible, when employing the mages against other nations, you could see some internal dissent from mages who were originally from those nations, being asked to attack their own people.
Another consideration, I mentioned in passing earlier, is attrition. In the real world, any military action will come with losses for both sides. In your case, this means your nexus state could find itself into a prolonged conflict eroding its power. So, while a single incident wouldn’t bring them low, years of campaigning on multiple fronts could wear them down.
Having a scenario where 500, magically empowered warriors have completely tipped the balance of power in their world won’t make, or break, the reader’s suspension of disbelief. The world you create will do that.