Can I run an external frame-mounted fuel pump for a 5.3 swap instead of in-tank pumps?

Yes, as long as it's done right:

• Mount it low, below the tank, so fuel gravity-feeds the pump. Electric pumps push well but don't like pulling fuel up out of a tank.
• Protect it from road debris and off-road hits — an exposed pump is vulnerable.
• Expect more noise and heat than an in-tank pump, which is cooled, lubricated and muffled by the fuel around it.
• Plumb for pressure: an LS needs about 58 psi. LS EFI needs about 58 psi vs 5–7 psi for a carbureted small block; parts-store hose clamps/rubber hose are not adequate at 60 psi. Use AN hardlines, push-on hose/fittings, or ethanol-safe hose (e.g., Earl's Vapor Guard).

Many builders still pick an in-tank pump for a street 5.3 because it's quieter and lasts longer. See is an in-tank pump quieter and more reliable?