It would be quite useful.
The two hard parts to teach warriors are intent to kill people you have never even seen before and keeping focussed while somebody is trying to kill you. Probably in that order. The second issue is fixed by simple experience, while there are apparently people who spent years at war firing in the general direction of the enemy without once trying to hit. I'd assume that many new soldiers with your technology level would concentrate in defense to the point where they would be no danger to their enemies.
In your scenario you send the fresh young warriors to the field to prove their manhood and make sure they all "show the right spirit". So your actual fighting force would be entirely composed of people who have already proven they have overcome those two big issues. And they'd all know it too. So the morale would be on par with veteran troops I think. You'd still need proper equipment, tactics, and weapons training, but unless you are inferior in those or just plain old numbers, you'd probably win any fights. Unless you run into to professional troops, such as Roman legionnaires, or your opponents are real combat veterans. And even the Romans usually had issues with high morale opponents.
I probably should explain a bit here. The battle was not usually decided by killing opponents, it was decided by the morale of one side breaking, at which point their formation broke. After which the real killing started. So the big differentiator is ability to keep discipline in combat and veteran or professional forces have a huge advantage here. In many colonial wars (or wars Romans had millennia before) the opponents had superior numbers, much better motivation, similar equipment and were just as brave. And still were soundly defeated simply because European (Roman) forces could keep formation longer.
So your "kill or be killed" play wars could give a big advantage. If...
Do not waste already proven warriors. Seriously. Make it an initiation for becoming a warrior. Expected of all males once they reach certain age. But not compulsory, a boy who doesn't want to be a warrior and is willing to take the reduction social status or has another calling such as a blacksmith, a priest, or shaman should be allowed to. Similarly there is no real reason why a girl who demonstrates skill with weapons would be prevented from proving herself.
It is a religious ritual. It should start with a solemn ritual by the leaders and priests of both tribes. The warriors should be blessed and clearly marked with something like body paint or ritual dress. And given the specific weapons used for the initiation. So no armor or ranged weapons, even if such are usually used. Instead short spears or swords that require getting up close and personal. Should be nicely decorated though. And once it is over both the survivors and the casualties should be blessed in shared ritual by the two tribes.
Older, already proven warriors would participate and go along to give advice, instructions, leadership and so on. Basically act as NCOs to make sure inexperience does not result in an embarrassing failure of the ritual. But they would not fight and attacking them would be forbidden.
Realistically, while male mortality is much more tolerable than female mortality since it has much less effect on fertility, it would be unsustainable to do this for the whole male population. So instead this would something for the elite warriors. Instead of initiation to become warrior and full adult, it would be for membership to elite warrior society that in war becomes officers, leaders, and elite troops. During peace they would be the personal guard of the king or similar privileged position. So there would be enough incentive to risk your life.
Alternately you could take steps to reduce mortality. There was recently a question on serrated weapons and in my answer I noted that such a blade can be made so it makes messy but shallow wounds and be coated with a substance that acts as both disinfectant and makes the wounds hurt like hell and scar. Such weapons could be scary enough to fill the purpose while having low enough mortality for the initiation to be near universal.
Not sure which suits your vision better.