Adding the Wurst Client to your mods folder in a CurseForge App profile should work, as long as that profile uses the Fabric modloader.
The CurseForge App itself is just a launcher, so it should not affect compatibility. You may have to dig a little to find where this launcher places your mods folder, but once you've found it the installation steps are the same.
If your modloader is Forge, that generally won't be compatible with Wurst, unless it happens to be Forge 1.12.2, 1.11.2, or 1.10.2 - in that case you can use ForgeWurst. Your Minecraft version might also make a difference, as some older versions can have very different installation steps.
I hope this clears things up a bit! If you are still having trouble, please let me know which modloader and Minecraft version you are using and any specific error messages you are encountering.