You clearly don't understand the KHL. Nobody puts up good production in the draft year there. It is notoriously difficult for young players.
It is a men's league, so typically not. Ovechkin is arguably the best Russian to ever play the game and even he couldn't put up a 0.5 PPG in his draft year (and he was only 2 days off from being eligible for the 2003 draft).
However, it is still possible for young players to have success in their DY and DY+1.
Typically, if you are on a really stacked team, you actually get better chances as a higher end prospect than if you are stuck on a upper-middle team. Usually those high end teams have so much high end talent that they can afford to let their young stars playing in lesser roles rather than experienced veterans, and their young stars are also typically among the best in their age groups as well.
The upper middle and bubble teams typically have good veteran talent throughout their lineup, but can't afford to play many of their young guys if they want to stay competitive. If you can crack that lineup as a younger player, you have a great shot at an NHL career, because you have to be better than guys who are many years older than you.
If you are on a crappy team, then typically they lack talent and so there are plenty of opportunities for young players. That doesn't mean you are good, but if you can play well on a team with little support, that typically looks good on you as well.