Maybe. Depends how sensitive the boat lift is to supply voltage - #10 copper at 14 amps for 200 feet is about 5.8% drop (or 7 volts) - nearly double what is normally designed for. But given 120V at the head end, that's still 113 volts, and many items are perfectly happy with 110-125V.
Is the 3 conductor #10 OUTDOOR wire? If it's indoor Romex, it cannot be used outside, even in conduit - the insulation is not rated for water, and all conduits outdoors are assumed to be wet (and the assumption is usually right.)
If you are buying wire, look at #4 or #6 Aluminum - it may well be a LOT cheaper than #6 or #8 copper, even if you have to buy conduit one size larger.
(not affiliated in any way, just one of the more useful/less-spammy sources of VD & Fill calculators - there are many others.)
When you are trenching for the power, consider dropping another conduit (even 1/2" could work) in case you decide later that you'd like WiFi at the dock area. No need to run wire now, but you'll kick yourself later if you don't, and it won't cost much to add.