Yes, it is related, but it is not equal. It depends on what you do with it. If you spend $1k on phone calls or letters, it won't be nearly as good as if it was spent on home visits or campus visits. Most everyone agrees that campus visits are the best bang for your buck... outside of promised starts/playtime at least.
Also, your $1k might be completely different than my $1k. Distance is a huge factor that you can see. Coaching prestige is also a big factor that you cannot directly judge. If you are a constant top 10 team, and I'm a new bottomdweller, your $1k will mean a lot more than mine.