Alexander M. Haig Jr.'s recent track record in the business world raises serious questions about what kind of president he would make.

During his four years on the board of directors of Allegheny International, the Pittsburgh-based conglomerate has been beset by Securities and Exchange Commission charges, which the company did not contest, as well as a flood of shareholder lawsuits claiming mismanagement and misappropriation of funds by company executives and directors, and a New York Stock Exchange threat to delist the company.

There is nothing to suggest that Haig ever claimed to be or was in fact in charge of Allegheny, which primarily manufactures consumer appliances among other products. But he was closer to the action than some, serving on the directors' executive and finance committees, which work closely with company management. And as a former chief executive of United Technologies, Haig might have been expected to have at least an inkling that a once-vibrant corporation was virtually crumbling around him.

The SEC investigation of Allegheny began shortly after a Business Week story in August 1986. The article questioned the company's business practices and the extravagant fringe benefits it gave to its executives while its net worth and stock price plunged and its operating losses soared.

Two months after the critical article appeared, Robert J. Buckley resigned as Allegheny's board chairman and chief executive officer.

On Sept. 9 of this year, the SEC filed suit in federal court here, citing Allegheny's violations of security laws and seeking an injunction to force corrective action by the company. Allegheny signed a consent decree the same day, admitting no wrongdoing but promising not to commit any more violations.

According to the uncontested allegations in the SEC complaint, which has been studied by our reporter Frank Byrt, basic accounting records and internal controls were not maintained from 1981 to 1985. This resulted in material misstatements of financial worth in company reports, the SEC said.

Among the abuses, the SEC said, were:Use of the company's five jets (the "Allegheny Air Force") for personal trips by executives and directors. Purchase of more than $100,000 worth of wine for personal consumption. Use of company-owned automobiles and luxury condominiums for executives' personal pleasure. Financial and legal services obtained by executives at company expense.

The uncontested SEC complaint also accused the company, its officers and directors of making "false and misleading" proxy statements to shareholders, by failing to report their personal use of company assets and their part in company transactions from which they benefited personally.

In addition to the $20,000 a year Haig is paid as director, he also received $50,000 a year as a consultant, until August 1986, the month the Business Week story appeared. A company spokesman said the consultancy was terminated at that time "by mutual consent."