A qualified 'yes'.

It should definitely be done, but there are three ways to do it. I would only consider two of them.

There's a pressure bleeder that hooks up to your brake fluid container and pushes new brake fluid through the system. There's a vacuum bleeder that hooks up to the caliper bleed and pulls new brake fluid through the system. Then there's the old-fashioned method of having someone sit in the driver seat and pump the brake pedal to build up pressure while someone else bleeds the brakes.

The first two would be fine, but they'll take some extra equipment you may or may not have. The last one is almost guaranteed to damage the seals on your calipers after 20 years of sludge buildup. Forcing the piston and seal to go well beyond the normal range of travel with crap in the way is a recipe for damaged seals. If you don't have the equipment and don't want to buy it, take it in to someone who does have it and will use it. I got a pressure bleeder for less than $100 and it does a beautiful job. I also got a hand vacuum pump for less than $30 and it included a kit to vacuum bleed the brakes.