No. Things speed up the more subscribers you get but there isn't some magic number where things suddenly get faster. Things just snowball. Getting from 0 to 50 subs is harder than from 50-100. Getting from 100 to 200 is easier than 0-100. From 1000 to 1500 is easier than from 0-500, etc.
The larger you grow, the more people you have sharing your videos, and the more videos you have through which people can discover your channel. On top of that, lots of high quality views with good audience retention will mean that your videos rank highly in search etc, which will drive in yet more of those views.
Growth on YouTube directly causes more growth to happen. It's why when a channel blows up in popularity it can typically happen very quickly.