I haven't played Skyrim since January, and I don't even think my PC has been booted up since March.
After I boot up, update, defrag, etc to my PC, do you think I would be good playing Skyrim with the current patch, but my mods from January? It'll take me a pretty long time to update them. Should I run into any issues?
Mods and Patches. Fun times. Any and all mods need to be looked at to see if they are compatible with the current patches. Some mods will not be affected, some will.
You can provide a list of your mods in the Skyrim Mods section and perhaps those folks can tell you which mods are broken by the patches. The other thing to consider is no mods that came out before the end of February were made with the official editor, so you may want to replace most of your mods anyway.
I was considering just deleting my Data file and letting Steam re-download it. There were few mods I actually cared about that much, so it probably won't be that big of a deal to go and retrieve them.
Yep, start afresh. If you're deleting your data folder anyway, then it's probably also a good idea to clean up those "hidden" files too - have a look at c:/users/username/appdata/local/skyrim - files relating to your plugins and load order are also stored here, so for a clean sweep also delete dlclist.txt, loadorder.txt, plugins.txt and steammodlist.txt