No, it's not realistically possible to completely bypass the power steering system on a 1998 Ford Taurus and still drive safely. The power steering pump is integral to the system; removing it will leave you with only manual steering, which would require immense force to turn the wheels, especially at low speeds. The steering wheel would be extremely difficult, if not impossible, to turn.
While you could theoretically disconnect the power steering pump, doing so would render the car undriveable for all practical purposes. It's a significant safety hazard. The only way to "bypass" it would involve a complete replacement of the steering system with a manual one, which is a major, impractical, and unsafe undertaking.
