No, there isn't a magic number where your videos start ranking better. It *is* however true that it gets easier at 100 subscribers, and at 1000 subscribers.. but it also gets easier at 99, and 101, and 143, and so on. With every additional subscriber you have (assuming they're real subscribers and not dead subscribers/sub4subs), that's more traffic driven to your videos. More traffic driven to your videos in those first 24-48 hours of release mean you have a higher chance of ranking for your chosen keywords that you decided to target.
So as you grow, it will speed up. To put it in perspective just how this snowballs as you get bigger, the time it took me to go from 10,000 to 15,000 subscribers was about the same time as it took me to go from 0 subscribers to 46 subscribers (actual stats that I checked in my analytics).