Yeah, Elite has Solo mode, Open which is more-or-less MMO, and you can have private groups as well.
It's always online just to sync the economy/politics/etc. though - it doesn't use much data if you're playing in solo mode, but you can't play completely offline.
Open uses a lot more data when you're actually instanced with other real people, but the galaxy is so big this is still relatively uncommon away from certain busy systems.
On the complexity front - I should point out that it's simple compared to a flight sim, but there's a lot more to learn than the arcade flight model of No Man's Sky. The inventory system is a lot less painful though.
Oh, and I played about 22 hours of No Man's Sky before un-installing and leaving a bad Steam review. A lot of it is perfectly nice, but that inventory system really is appalling. Still not terrible value if you get it on sale, though, and YMMV.