He's facing one of the deadliest swordsmen in Westeros on foot, so, no.

The resulting battle was brief. The Lannister horsemen made short work of Eddard's men, cutting them to pieces. Jaime turned to one of his men. "Give Her Grace your cloak," he said. "She's been shamed long enough."

Eddard watched as Cersei clothed her form in the offered cloak, sneering at him. "You were a fool, Lord Stark! Did you honestly imagine it would be so easy? You should have sided with us!"

Ser Jaime nodded. "I'll give you this one chance to surrender, Lord Stark. And if you do not take it, I'll have no mercy."