I don't see why not. It doesn't mention that you need to be staying onsite in any of the info. I've found:
Junior Fishing Excursions
(Kids' Fishing Around the World)
The Junior Fishing Excursion is a one-hour long excursion available for guests ages 6-12.
Pickup is available from the following resort marinas and locations:
Contemporary Resort
Sat. & Sun. only; 10 - 11am
Polynesian Resort
Sat. & Sun. only; 10 - 11am
Grand Floridian Resort
Sat. & Sun. only; 10 - 11am
Wilderness Lodge & Fort Wilderness Campground
Sat. & Sun. only; 10 - 11am
Yacht & Beach Club Resorts
Mon. - Fri. only; pickup between 10 & 10:15am
Community Hall at BoardWalk Resort -- BoardWalk Villa side near the quiet pool
Mon. - Fri. only; pickup between 10am & 10:15am
Call the Resort Recreation Reservation Center at (407) WDW-PLAY (407-939-7529) for reservations and information.
Ages: 6-12
Price: $28.16 (plus tax) per Guest
Locations and Times: Pick up areas may vary - please call for hours and locations
Guests may not bring their own food, beverage, or coolers aboard.
You can also go to POR too for some more relaxed fishing:
The Riverside Resort also offers a catch-and-release fishing on Ol' Man Island at the Fishin' Hole. Hours are 7 a.m. - 3 p.m. and vary seasonally. The Fishing Hole is stocked with catfish, bass, and blue gill, and a catch is almost certain.
Cost -- Cane Pole & Worms - $4/hour OR Family Fishing - $12.50/hour (up to 6 people)