Would the British still get Lafayette, then?
I'd say 75% chance. Some unlikely things can happen. in the Crimean War, a British cavalry unit, the heavy brigdate, charged a unit three times as big as them and won. The Light brigade charged an artillery battery the wrong one) across a mile with no cover and with an artillery battery to one flank and for 100 meters, batteris on both flank. The charge overran the battery they were charging before being forced back.
Likewise, in the war of Austrian succession, one officier braved seven days behind enemy lines before reaching friendly territory... after losing a battle.
most likely, the most probable thing happens and Lafayette gets captured, or perhaps a stray bullet hits him if the defenders try to shoot the British (before realizing they are hopelessly outmatched) and the British shoot back