Depends. Look at the graph of month year of professional hockey player[1]. Player born in first quarter is twice as more likely to be in pro leagues than last quarter. Month of birth's only effect is that it gives 0.5 year extra during junior year to be in spotlight. It shouldn't affect player's performance in any other way. And the effect persists for decades.
If you get supported initially when you aren't the best, the effect of the small support can make you much better player.
[1]: https://www.lockhartjosh.ca/2017/11/hockey-birth-month-why-i...
In the US, USA Hockey (by far the biggest youth hockey organization) groups players by birth year. So if you are born late in the year, you are among the youngest players on your team. You tend to be smaller, and less experienced, and unless you are exceptional you tend to play less. This impacts you from your first youth teams up until high-school.