Has President Reagan unwittingly done federal workers a favor by proposing to cut their pay 5 percent, and keep them on the job Christmas Eve?

Did the Great Chicago Fire of 1871 (supposedly started by Mrs. O'Leary's cow) actually aid the cause of urban renewal in the Midwest?

Federal workers now, and Chicago residents then, probably would answer "no" to the above questions. But it has been said that every cloud has a silver lining.

Consider the proposed pay cut: Many Americans think that federal workers have it made. Despite studies showing that the average civil servant (salary, $25,247) is paid between 7 percent and 18 percent less than his counterpart in the private sector, many in the private sector are unmoved.

Arguments that the government is a highly professional corps of people who do vital and sometimes dangerous work, rather than an army of paper-pushers, don't impress many Americans who do not work for or appreciate the work of government.

According to the Bureau of Labor Statistics, 27 percent of the American work force represented by unions did not get pay raises in 1983 -- or in 1984. Six percent of the workers, the bureau said, took pay cuts so that their companies could stay in business.

People whose pay is frozen or cut are unimpressed -- and sometimes write nasty letters to newspapers -- when they hear that government workers are getting raises of only 3 1/2 percent or 4 percent. They don't care or believe that the feds are underpaid or that they perform jobs essential to defense, health and safety. To somebody who gets nothing or takes a pay cut, a raise -- no matter how small -- is a raise.

There is a very good chance that Congress will reject the president's proposed 5 percent federal pay cut, as well as the suggestion that members of Congress set an example by taking a 10 percent cut.

But the fact that a federal pay cut is being considered cheers a lot of people outside the pro-civil-service Washington area. It might (if you believe in silver linings and the tooth fairy) make them think that feds are real people, too, who sometimes take it in the neck when their company is in the red.

Or consider that extra day off at Christmas: Many federal workers are furious that this year Reagan ignored the customary White House practice of giving feds an extra day off whenever Christmas falls on Tuesday or Thursday.

A lot of government workers see it as a grandstand play and note that the president will be on vacation in California over Christmas. If he wants to save the government money, they say, he should stay in town, save the jet fuel, and work.

But many nonfederal workers don't understand the feds' anger or expectations. Lots of stores will be open Monday, Dec. 24. Lots of businesses will be open -- with some having Christmas parties after work to ensure that people show up for work. For many non-feds who want the extra day off, vacation is the only way they will get it.

"What makes your federal 'constituents' think they are different?" a Lanham businessman writes. "Of course, many merchants wish government workers were off that Monday so they would shop. But I would like to make the point that we can't stay in business unless we are open for business. . . . The pressure on us to give our employes a bonus holiday is tremendous when our workers see the federal government shutting down.

"I, for one, admire the president's decison. If the civil servants want to take a day off with pay, let them . . . pay for it like the rest of us."

If the 5 percent reduction in pay did go through, would we see civil servants wearing T-shirts saying, "He Cut Mine Off, Too." Will others read, "I Worked Christmas Eve." If so, will anybody out there care?