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).
Just to add to @JesusGreen, momentum also plays a big factor on whether things will get easier or not. If you're not active for a very long time or your uploading things your viewers don't like, your subs will forget about your channel. So your actual sub count doesn't really say much.
I don't know about YouTube search algorithms related to sub count or anything, but channels with less than 100 subs (or 1000) look less attractive in some way. Let's say that, next to the banner and the profile pic, the subscriber count is also quite a "lure" if it's over 100 or 1000
When I hit 100 I started to gain traction, and get slightly more views and my subscriber growth increased. I probably get anything from 2-10 subscribers a day right now. Might be down to the algorithm doing something, I have no idea haha
Closing in on 100 subs so I guess I will find out. I imagine the only way I can tell is keeping an eye on my TubeBuddy keyword rankings and if they start to improve then there may be some truth to myth.