Nothing about this presidency is appealing to progressives, but simply getting Bernie's email list isn't really going to change anything on its own. The people who signed up for Bernie's mailing list who aren't currently signed up for the DNC's mailing list aren't going to magically get involved with the DNC when they start getting emails from them. Faith in the Democratic party establishment is at rock bottom with people further left than the party platform. It's going to take a lot of work to win people over, and that should probably start with making an earnest effort to 1. show any signs of life fighting against the GOP (Schumer has made it pretty clear this is not in the playbook yet) and 2. vocally outlining plans to address issues important to the far left, particularly labor and social issues.
The DNC has done a pretty woeful job of riding any sort of social issue waves recently. They were tepid at best getting on board with BLM. The ACLU made far more noise about the immigration ban than any official party response. They approved of The Women's March from the sidelines, but that's about it. They let the GOP walk all over them during the cabinet appointment process, purposefully avoiding being seen as "obstructionist" and then letting the fight they viewed as the most important to win, Sessions, slip through their fingers, with only Warren daring to really step up to the plate and show any signs of life.
The left is getting away from the DNC, and they just don't seem to know what to do about it. Granted, it may seem oddly petty for Sanders to not hand the list over given that it's a fairly common gesture, but I don't think it'd really change much. If the party wants the attention of those people, they need to start doing something to engage them in the first place. It's all well and good to say "but there's a monster in the White House and we all need to do our part!" but the DNC itself doesn't exactly seem to be taking much action in this regard. Until the DNC proves they can fight, the disenfranchised will be fighting without them.