Yes, neutrality in war is a valid strategy if there is enough of a disparity of resources between your superpower and the less civilized warring nations.
Based upon the scenario you've given us, it sounds like we're at the start of the Scientific revolution. Your Superpower probably has not only an advantage in native resources, but also an influx of wealth and a resulting knowledge gap. Such a society would progress far more rapidly than its neighbors, quickly becoming a fearsome presence much like the major empires (Hittite, Assyrian, and Egyptian) of the Bronze Age.
In the real world, Europe was so broken up historically with tribal/royal warfare that no one maintained a monopoly on resources or knowledge long enough to exploit it effectively. Perhaps the best correlate, both geographically and technologically, would be the Ottoman Empire, which was at the height of it's power at the start of the 17th century. Without a Russia on it's northern border or the religio-cultural strife caused by the class distinctions between Christians and Muslims, the empire might well have retained it's full power into the 19th and 20th centuries.
If you've got resource poor North and South separated by a Mediterranean, your resource rich Superpower would want to supply both sides with raw goods to fuel their own economy. Then, when the war dies down, they flex their muscle against the weak winner and expand their territory. The institutions of learning in your progressive Ottoman empire can't be mirrored in your surrounding medieval societies which are basically struggling for everyday sustenance and border squabbles.
Since most people in the warring lands would be illiterate (as historically they were), your advanced empire wouldn't need to worry as much about knowledge leaking across the border - not enough people would have the resources, background, and technical skill to replicate their more advanced technology, especially if there was a linguistic barrier on top of everything else.
The political ramifications? As an important crossroads between north and south, They would be courted for favor by everyone. If there's a threat, it's probably from the more stable Western nations banding together to challenge supremacy of your Superpower, since they share similar advantages for trade and war as the single nation, and it might be easier to play one minor nation against the other rather than dealing with a monolithic superpower.
Ultimately, though, I think your "middle" nation is doomed to fail from the Superpower mopping up after the civil war and the opposing western nations seeking to expand their holdings. The resulting collapse of the middle nation would result in an east-vs-west clash, as your border countries expand toward your superpower and the "inner" western nations (who can't expand into the middle kingdom) will diplomatically plead the superpower into conflict with their neighbors so they can expand themselves. The result of this evolution in conflict is outside the scope of what you're asking, though.