No, this will not work, for several reasons.
Few citizens will volunteer to die in 'glorious' battles merely for the honor of their local ruler with no actual threat. So these armies will be based on draftees and will probably be a burden on the province, leading to unrest (like the 'Hunger Games').
The cost of fielding large armies on a continuous basis will bankrupt the empire. War is the most expensive operation an empire can do, if there are no external resources to acquire (land, minerals, slaves, etc) then how can they afford it? In times of peace empires typically shrink the army and spend on domestic programs for this very reason.
What the wise men of Toren are doing is enabling a coup. Letting local leaders raise what are essentially private armies and compete in battle will just select for a charismatic general who will now have a great army to take over the empire. Preventing this is one of the main reasons Rome had strict rules on where and when generals could move their armies around the empire (hence the violation when Ceasar brought his legion "across the Rubicon").
Even if these competition battles occurred, they would not guarantee success against a new threat because tactics and weapons would presumably be static and not matched against the new enemy. Fighting yourself is great but no substitute for conflict with an enemy that has novel weapons and tactics. Medieval warfare was not terribly complex in the grand sense, it relied more on individual skills (cavalry, man-at-arms, archery, etc) and very basic "follow me!" tactics. So constant practice of large unit maneuvers wasn't really necessary.
So in theory your premise would work in retaining skills between conflicts. But in reality without continuous expansion an empire can not afford or even justify a large army. Internal suppression is usually the main requirement for a large force, but even then skillsets are on the decline because there are usually significant force imbalances between the standing army and areas in revolt (if the forces are comparable, then there really isn't an empire except on paper).
What may work is a small cadre of experienced soldiers who can quickly bring in raw recruits, give them some basic manual of arms and drill training, and then lead them into war. This small cadre could hone their skills in realistic training and small skirmishes with barbarians at the edge of the empire. This would limit their cost, give the empire the ability to raise large levies in a time of need, and maintain an adequate control capability of leaders familiar with each other and that share a common command structure. An established war college and codified military doctrine would also help transmit information from generation to generation, something few pre-industrial civilizations could do.
Basic warfighting skills can be incorporated into local games, athletic events, and competitions. The longbowmen of South Wales were like this. They made the weapon a part of their daily culture so when needed, there were trained archers available. The citizen-soldiers of Greece were the same way. They would gather on occasion and practice small unit drills so each village could produce a unit of hoplites. There was often a short period of compulsory military training in adolescence that was part indoctrination into military culture and part labor force for whatever construction/garrison projects the region needed doing.
So you can have a small cadre of trained leaders with a large pool of mostly capable citizens to form instant armies at a fraction of the cost of maintaining standing armies just for practice.
Maintaining this for centuries of peace will also be problematic, if only that it is very difficult to keep anything going for that long, even without external invasion. Resources run dry, natural disasters happen, technological development overturns the established order, folks try to take power, etc.
If you DO go this route, look at feudal Japan under the shogunate for an idea of how military forces might transform in an insulated society of very curtailed warfare. It also wouldn't surprise me to see a society such as this being ruled under a religious theocracy since it would need a very secure system of transmission of rulership to maintain centuries of continuous rule.
The generals in these battles would have to be carefully selected (which works against the military meritocracy you want in order to have the best warriors) or they would have to be tightly controlled. Again, in Japan, the local lords were forced to keep family in the capital as insurance against revolt. This way your ruling class, whatever they may be, can have some measure of protection against a famous successful general staging a coup.
