Yes-- but in the South End, considerably earlier than the 1940s. Here's a description from the 1906 publication, the Lodging House Problem in Boston.

"Every effort was made to make the district attractive. The houses were extremely well built for the period and no expense seems to have been spared to make them elegant, and in many instances even luxurious. Provision was made for parks, and some of the prettiest places in Boston to-day are the little parks and "squares" of the South End lodging house district. Especially may be mentioned West Chester Park, Worcester Square, and Union Park. For almost a quarter of a century liveried coachmen and white-capped nursemaids airing their charges were a common sight on Tremont Street and other thoroughfares, while the cross streets were gay with the voices of children. The South End, then, was once a city of private homes; now it is a wilderness of factories, tenements and lodging houses. Fully five sixths of the old residences are now rooming houses."

The writer says that as Back Bay was filled in, South End people began building houses there. Wealthy families trickled out of the South End gradually in the 1870s then got out like rats through the '80s. By 1890 the movement was finished and the South End was predominantly lodging houses.