The script extender (supports The Elder Scrolls IV: Oblivion and Skyrim; Fallout 3, 4 and New Vegas) is borderline mandatory for modding the supported games. Does Mod Organizer have any deeper integration (automated installation, update notifications) with the script extender or do you have to install manually and keep track of the SE updates by yourself?
Mod Organizer can only access the Data folder. Since Script Extender needs to be installed directly into the main game folder, there is no way to let MO organize it. Manual installation is still the only way to go.
However, you do get a warning within Mod Organizer whenever you have updated the Script Extender or installed a mod dependent on a newer version, since the game likely won't load properly (that's with Skyrim (SE), at least - I think it gave me a .dll-warning after I had updated SKSE without updating the dependent mods).