No CF-number unless powered (someone already said that).
According to DMV, as I read it, drinking while operating a paddleboat would (or could) be A BUI:
http://www.dmv.ca.gov/pubs/vctop/appndxa/harbnav/harnav655.htm
(Or more specifically, as I read it, operating with an open container or smelling of booze gets you tested, testing 0.05-0.08 is suspicion of BUI, and 0.08+ is BUI)
Unlike ground-based transportation, where CA differentiates between a motor-powered and human-powered vehicle (e.g., bicycle), the use of the word "vessel" and no mention of power source seems to put paddleboat in the same class as motorboat or sailboat.
What's more, certain areas (such as San Diego Beaches) have recently re-worded their ordinances to go after people who try to circumvent the beach alcohol bans by floating on tubes just off the beach and drinking. That'd be a big fine. May want to check with the lake (or local authorities) or whatever Park it may be a part of on such ordinances.
EDIT: yes, a paddleboat is a "vessel":
http://www.dmv.ca.gov/boatsinfo/boatreg.htm