Correction: At the Atlantic Yards site (and others), a Project Labor Agreement (PLA) would have averted a strike
Not so. The arena construction, and the rest of the work, is governed by a Project Labor Agreement (PLA), which, as Gary LaBarbera, president of the Building and Construction Trades Council of Greater New York (BCTC) reminded members, includes a no strike/no-lock out clause.
Here's a list of such projects.
As one commenter on the Local157 blog pointed out, informational picketing would be permitted.