That would get you an exact copy of the disk with everything on it. And also, while 200 DVDs sounded a lot, it's "only" 860GB (assuming 4,3GB/disk which I think is the most common for movies), so it's not stupidly expensive either. Obviously you'll want a RAID setup and most likely backups for that, so it's more than just a single 1TB drive, but still quite manageable.
Majority of the data (video) is already compressed as MPEG-2 so I'd think it doesn't compress very well. But if you don't have enough storage it's always an option to re-encode video with something more modern and achieve smaller file sizes from that. But that also removes at least DVD menu and other 'format dependent' options.
I used K3b for that. It can copy to image and even ignore errors if necessary, though I didn't yet have to try that. It's 8.5GB per disc, so get some 2TB HDD for that.