Is it absolutely necessary to use a brake scan tool to bleed the brakes on a
1998 Chevy S-10, 2.2 motor, 2 wheel drive? I know that there is air in the
modulator because the right rear line blew and the master cylinder ran dry
in the front resevoir.

Yes, it is absolutely necessary to use the scan tool. Without performing the "automated bleed", you'll never get all of the air out of the ABS unit.