The IGN Wiki states that you do need an Internet connection even if you do not play with friends. It will require the UPlay code provided with the game, but not a UPlay account to use.
The good news is the only resources that carry over into the game are Reales earned. The other resources in that game are just for upgrading your fleet or completing more fleet missions.
You can also unlock some art and treasure maps. Art shows up in your house at the Pirate Cove. Most of the treasure maps just lead to more chests with Reales. The notable exception to this is the plan for Elite Fire Barrel Storage, and I personally never found Fire Barrels to be terribly useful in combat.
So yes, you need an Internet connection to access Kenway's fleet, but aside from some vanity items and the Elite Fire Barrel Storage you are only missing out on another source of income and a mini-game. This has no affect on the story.