The copious smoke that clouded many of the issues in the hotly contested effort American Express Co. made to acquire McGraw-Hill Inc. may never clear now that American Express has withdrawn.

Was American Express President Roger H. Morley guilty of at least ethical improprieties by serving on the giant publisher's board at the same time his company was contemplating buying McGraw-Hill?

Should Morgan Gauranty Trust Co., long McGraw-Hill's major bank, have been the bank coordinating the takeover financing for American Express?

Did an American Express takeover of the publisher pose the First Amendment problems that Chairman Harold W. McGraw Jr. and many Business Week editors and writers claimed?

These are among the major questions that will go unanswered now that American Express has withdrawn its bid and both companies have canceled all pending litigation in the case (although there are outstanding shareholder suits against McGraw-Hill).

But companies, shareholders and the acquisition experts in Wall Street should learn one lesson well from the abortive merger:

Washington can be expected to become increasingly important as a factor in corporate takeovers.

Entrenched managements that wish to insulate themselves from an acquisition may find federal regulations and Congress a better weapon than appeals to shareholders and the Securities and Exchange Commission.

Harold MeGraw and those he hired to fend off American Express' advances -- including the famed acquisition lawyer Martin Lipton -- made brilliant use of the federal government to thwart the American Express bid.

It is fair to say that their hand was strengthened when American Express showed it had not the stomach for a hostile takeover try and withdrew to the sidelines, hoping the threat of either a proxy fight or suits from angry shareholders would convince McGraw-Hill and its board to put the generous, $40-a-share offer to its stockholders.

But by the time American Express bowed out all together, on March 1, the federal bureaucracy had waded deeply into the affair:

The Federal Trade Commission mounted an inquiry into the proposed takeover and said it was concerned, among other things, that the conflict of interest that could occur when a diversified financial corporation such as American Express (that makes most of its money off travelers checks, credit cards and insurance) acquired a publisher of financial information.

House Banking Committee Chairman Henry Reuss (D-Wis.) asked a subcommittee to study the proposed merger to see if banks should be making loans to companies that want to buy other companies, when there might be more useful ways for institutions to lend their funds.

The federal Communications Commission had the acquisition on its agenda because McGraw-Hill owns four broadcast properties.

Looming in the background was another question prompted by McGraw-Hill's defense men: Should American Express, which runs numerous bank-like services and owns a foreign bank, be exempt from banking regulation in the United States.

It is not as if Washington has never been a factor in mergers. The Justice Department and the FTC always are concerned if an acquisition seems to present antitrust problems. Indeed the Justice Department agonized long and hard before it permitted the parents of two major steel companies -- Lykes and LTV -- to merge last year.

And Sen. Edward M. Kennedy (D-Mass.) is conducting hearings to determine whether the government should make size per se, not merely market share, a consideration in mergers.

And certainly the concerns raised in Washington about the McGraw-Hill-American Express merger were legitimate.

But the success of Harold McGraw and his hired guns in using Washington as a bulwark in its defense should encourage other incumbent managements to use the federal maze to discourage hostile suitors.

As one Wall Street observer noted, it was almost as an afterthought that McGraw said American Express' initial $34-a-share offer (later increased to $40) was too small for shareholders.

His initial comments centered on the alleged illegality of the takeover, the threat to the First Amendment and his personal pique at American Express and its chairman, James D. Robinson III, and President Morely for daring to make the bid in the first place.

American Express officials say privately they could have won a hostile takeover flight if they pushed it, but were afraid they would be left with a bitter and empty prize unless McGraw-Hill stopped fighting.

That may be so. But clearly, to a company that makes its money off public trust and without the interference of federal regulation, the thought of congressional hearings into the takeover as well as into American Express' exemption from banking regulations would have been more than the company could tolerate.

Government's role in the conduct of private business has grown steadily for decades: Environmental regulations, health regulations and most recently, voluntary wage and price guidelines are among numerous intrusions the federal government has made.

Business began to recognize this years ago. Trade associations by the dozens have mved to Washington. Nearly all major corporations, including Amercian Express, have elaborate or not-so-elaborate lobbying operations, And the prestigious Business Roundtable -- a group of chief executives of major corporations -- makes its ponderous policy pronouncements from Washington.

Now, as the McGraw-Hill episode shows, the merger specialists are waking up to na new world of Washington as well.