Not necessarily. The kid getting the college scholarship for baseball on my son's team is the one with passion and discipline and ability - but he has a single Dad for a parent where there has never been money. He played park and rec ball - not travelling - through middle school, joined the high school team, and plays VA ball in the Summer.
Our high school basketball team is not full of the white well off kids that make up 40% of the school - whose parents had them coached and had them on travelling teams in eighth grade, but full of the kids who have been playing pick up basketball - the kids from the part of town where darker skin and free lunches are common. There is an annual scream fest every year at basketball tryouts, when the parents who "invested" in basketball every year see their kids cut in favor of a bunch of black kids who don't quite know the real rules because they've never played organized ball.
The girl we sent to State for voice last year hadn't had a private lesson until the choir teacher started donating time in order to get her to State.
If a kid has the ability and the discipline, pro coaching and expensive equipment might push them a little farther. If they don't, you can throw money at it all you want and have kid who isn't very good.
Where expensive equipment is a requirement - its often more to keep the riff raff off the team instead of making the team better. Expensive soccer uniforms keep the players from having to play with the kid with a single Dad whose Mom took off and died of a drug overdose - in our case, its baseball and that kid is the one getting the athletic scholarship.