BY merging with Shawmut National Corporation, the Bank of Boston Corporation may once again become New England's largest bank - but probably not its strongest.The deal, expected to be announced any day, will be the latest in a series of large bank mergers since last April, when Fleet/Norstar Financial Group Inc. won the bidding to acquire the failed Bank of New England. Unlike the Fleet buyout and other subsequent deals, this one will test the efficiency of "putting two weak banks together - does it make one strong bank?" says James Howell, former chief economist with the Bank of Boston. Steven Felgran, a finance professor at Northeastern University, says the deal will "produce a bank that will certainly be a more solid institution" than either of the companies would be on their own. The two banks are struggling under the weight of problem real estate loans. Fleet, based in Providence, R.I., was not hit as hard by the slump. And when Fleet acquired the failed Bank of New England, the federal government took on that bank's bad loans. Fleet leapfrogged Bank of Boston to become the region's largest bank with $48 billion in assets. If regulators allow the new merger, Shawmut, based in Hartford, Conn., and Bank of Boston will be able to "get back on their feet quicker," says Gerard Cassidy, vice president of Tucker, Anthony, a brokerage house. The banks are expected to close branches where service overlaps and streamline back-office operations, leading to an estimated 3,000 layoffs. But Mr. Cassidy says the cost savings - which he gauges at $280 million annually - would not be realized until 1994, assuming the merger wins final regu latory approval by next June. The deal may get preliminary approval this week, following a meeting Monday between executives from the two banks and federal regulators at the Office of the Comptroller of the Currency and the Federal Reserve. Regulatory approval "depends entirely on the extent to which they convince the Comptroller and the Fed that they have adequate capital," says Mr. Howell, who is president of the Howell Group, a consulting firm. The banks, backed by several Wall Street brokerage houses, plan to issue $625 million in new stock to finance the merger and rebuild their equity capital. "I think they will be successful in raising the stock," says Cassidy, who expects regulators will approve the deal as part of an ongoing consolidation among the region's banks. Earlier this month, the Bank of Boston agreed with the Federal Reserve to improve its financial strength and not pay dividends without the Fed's consent. Cassidy predicts more such mergers in New England in coming months. Five of New Hampshire's largest banks are either insolvent or bankrupt, and are now seeking outside investors to stay afloat. Cassidy says he expects Fleet and KeyCorp of Albany, N.Y., will emerge as the new owners of these banks in the next two or three weeks. The five institutions are Dartmouth Bancorp, Amoskeag Bank Shares, BankEast Corporation, New Hampshire Saving Bank, and Numerica Financial Corporation. Several Connecticut banks are also in trouble. While industry troubles are worst in the Northeast, consolidation is occurring nationwide among some of the largest banks. Recently announced mergers include BankAmerica and Security Pacific in the West, Manufacturers Hanover and Chemical Bank in New York, and NCNB and C&S/Sovran in the South. Merged with Shawmut, the Bank of Boston would become the nation's ninth-largest bank, with assets around $55 billion, smaller than these other merged institutions, but larger than Fleet, which is now the region's dominant bank. Cassidy says the merged banks "will mesh with one another quite nicely" because of their differing strengths - Shawmut in retail lending to consumers and Bank of Boston in wholesale business with corporations. "We will start to see some real [profit] numbers on the positive side ... in 1993," he predicts.