The fourball played nine holes at Innisbrook Resort, with Woods reported to have spent a hefty chunk of time getting used to the greens.
Woods has not played the event for 22 years, but slipped it into the schedule along with the Arnold Palmer Invitational ahead of the Masters at the start of April.
Woods, who will play with Jordan Spieth at the Valspar, was named a Ryder Cup vice-captain in September, but since his impressive return thoughts have turned to him competing in Paris this year.
Is there a possibility Woods could hold a dual role as player and vice-captain?
“I believe that it is,” Furyk said. “What Tiger and I have discussed, and he mentioned this a little in his presser in LA, I said we're going to do what's best for him, but also - and most importantly - what's best for the team. What's best for the team is the top priority.
"Hey, look, I'm a fan of golf and I'm a fan of Tiger Woods. I'd love to see him get in position to make the team on points, or get himself in position to be considered if he didn't make it automatically.
"We left our conversation on the topic of Tiger being a playing vice captain with this: let's Cross that bridge when we get to it. But it sure would be a nice problem to have."
If Woods did play at Golf National, it would be the eighth time he has represented the Stars and Stripes in the event.