Short answer: My SSE game currently has 926 active mods, and I'm still adding a bit at a time.
You didn't mention if you are running Skyrim LE or SE, but I'm going to assume SE for some of this information. Most of the Vortex info is the same regardless (except dealing with max mod limits).
When you say they are not loading, are you talking about the plugins? There are two "tabs" on the left side you need to keep track of when you install/enable/deploy. The first is the MODS tab. That is where you do those three actions. The one below it is the PLUGINS tab. It is possible for the mod to be installed, enabled, and deployed, but the plugin not be enabled. If that is the case, it will not load into your game. It is the equivalent of neglecting to check the plugin box on the original Skyrim LE vanilla game loader.
Also, in the PLUGINS tab you need to make sure it is sorting so LOOT has a chance to have it's say. If not, there is a Sort Now button at the top near the left.
When Vortex is deploying, you will see a circular animation next to MODS, and when it is sorting you will see it next to PLUGINS. Vortex can be configured to automatically enable plugins when the corresponding mods are installed/enabled/deployed, and also to sort plugins automatically afterward. But if it is not happening automatically you can just do it manually. I do it manually to give me better control over the process in general (I may not want it to deploy or sort right now).
The first mod limit you will hit when you do get up there in number is the max active plugins. Keep an eye on the top-right corner of the PLUGINS screen where it shows Active: xx Light: xx If the Active reaches 255 you are maxed until you do something about it (several options, topic for another thread). With 926 mods I have 194 Active plugins, 550 Light, and another 231 in a merged plugin (counts as one of the Active plugins). With proper care and attention to detail my game is perfectly stable at this level.
Speaking of proper care, as long as you are doing clean installs, DO NOT install Steam, Skyrim or Vortex in the default \Program Files (x86)\ folder. Create another folder like c:\games or something and install them there. That will keep Windows from tinkering with them and causing known problems.
Hope this helps.