No LR doesn't have the ability to search your drives and find all images. You have to Select the Source, the folders, your images are in during the import process.
Actually, Lightroom could find all iamges and videos for you if you select the hard drive as a source on import and include subfolders. But frankly - bad idea. To get organized you should first think about what kind of folder structure would work for you. I personally have them sorted into folders labeled place-year-month (e.g. "Paris 2016-01"), cos i'd probably remember the place, maybe not the date the picture was taken. Once you have everything sorted into folders which all live in one main folder labeled whatever you want (i called it "My Lightroom photos"), then import it into Lightroom. That folder can be stored anywhere you want, but even if you think your hard drive is big, i'd rather go for an external drive and back it all up to a second one.
After that ALL of your organization, renaming, keywording should definitely be done in Lightroom, otherwise it will lose track of your pictures and videos and you'll have to "tell" Lightroom where you moved the pictures etc.
Hope that helps