Do I need a U-Play account to get 100% completion in AC4?
100% of everything achievements/trophies, memory sequences, boat stuff, just anything to complete the game
You do need it if you want the uplay achievements, it will also make it easier for you to get 100%. You need some social community chests and to get these you need to be connected to the uPlay servers.
Also friends who find events can share these with you through uplay so you'll find things easier. For PS4 and PS3 for example if a friend finds a community chest he can share the location with you, you in turn share it with your friends and so on, causing a chain reaction.
All in all, it makes it easier for you.
Short answer: 100% game completion (for example as tracked in AC initiates) does NOT require the connection to the Uplay account for Achievement upgrades. But this is solely based on the progress tracker in game.
For Uplay achievements a Uplay account is required; also various ingame items (e.g. community event items) this account is is necessary.
Despite those two points, there is also some ingame content that does not require a Uplay account and does not count towards 100% game completion (computer hacks, sticky notes, database completion, cheat unlocks etc.).