Due to a hard drive failure, I now have to re-install Skyrim. I can get data from my old drive and was wondering, with a modded game (30+ mods) do I just need to get my Skyrim/Data folder and my savegames to continue play as before? I only had 3 mods from Steam Workshop and all the rest were from Nexus.

Technically, yes. Its a very dirty way to go about it though.

Yeah, that will work fine.
Mods only install to your Data folder and don't usually have any strings in the Windows registry so you shouldn't have any issues.