bottom line - the Solo mode works beautifully. the constant connection is only to update the universe at frequent intervals; it won't affect your controls in a bad way and if there are lag spikes, they don't seem to impact the game in any way. (who cares if the market prices update 3 seconds late?)
It's true that regular lag spikes make very little difference in performance. From what I've seen from a very fun few days of the comms pits in my street being full of water and having extremely unreliable internet, it appears that ED uses an arbitration system where specific activities trigger sync events with the server. Local instances appear to run entirely on your machine in solo mode, so you notice no lag during regular flight. However, once you perform an action that requires a sync event, that action may be cancelled or severely delayed based on what's going on with your link.
One of the synchronization events is picking up fragments and allocating them to bins in a refinery. I know this one for a fact, because I've lost a dozen fragments of 40% gold a few times from sudden disconnects as soon as I picked up the first fragment. Other sync events appear to be opening the galaxy map, system map, reviewing reputations, shooting fragments off asteroids (the point where the frag jettisons), and requesting docking permission.
Anyway. Yes, you do require a 100% always-available Internet connection. However, it can be laggy and inconsistent and solo will still work. But it needs to be always available, packet loss and disconnects will essentially destroy the instance you are in immediately. Not so great for mining.