According to Senior development director Chris Wynn and a job listing at Bioware, Mass Effect will have an online component in the upcoming game from the studio.
According to Wynn they are going to have it in the upcoming game. In Mass Effect 3 Bioware added an online co-op to the game. They did the same with the recent Dragon Age: Inquisition game aswell.
We do know at this point in time that the team is deep in development of the game. We will expect more to come from them after the cancelation of Shadow Realms.