There actually is a Dead/Hasidic connection.

One of the Chabad Houses in SF was nicknamed the Dead Head Chabad. If a Dead Head stayed at that Chabad over the Sabbath they were given free tickets to a non Sabbath/Jewish holiday Dead show.

The Dead Head Chabad Rabbi also influenced Lollapalooza and the bands Jane's' Addiction and Porno for Pyros frontman Perry Farrell (given names is Peretz Bernstein). For a short period of time Perry became semi-observant donning Tefelin (The black straps Jews put on their forehead and arm when reciting weekday morning prayers)regularly. During that time Farrell also released a solo album of Kabbalah inspired music.

Although it doesn't appear that Farrell maintained his religious observance for long, he did headline Purimpalooza in 2006.

Not related to the Dead (at least the band), but to Hasidim and an interesting although under publicized movement within Judaism, is the Renewal Movement.

Renewal is a modern (ie non-orthodox)blend of Hasidic spirituality and progressive social action.
Chris Ownens's blog links to one of its institutions, the Shalom Center.

Although I've never attended a Renewal Service I've been told B'nai Jeshurun in Manhattan (bj.org), which I've never attended either, is the closest Synagogue in the area to Renewal in practice. BJ started out affiliated with the Conservative Jewish movement but now positions itself as non-denominational. Two of its 3 Rabbis have Conservative Ordination and the other received her's from a Reformed movement institution.

Wikopedia offers a a primer on the Renewal movement.
http://en.wikipedia.org/wiki/Jewish_Renewal.