In this case, as you mentioned, から is a softener, for making the parting of ways not so harsh.
Without the から: a bit cold
じゃあ帰る
Alright, I'm going home.
With the から: adds the sense of "if there's anything else you want to talk about, please bring it up now, because I plan to go home now."
じゃあ帰るから(他に話すことがあるなら今話そうね。なければ、また会いましょう。)
Alright, I'm going home, so...(if there's anything else you want to talk about, please bring it up now, because I plan to go home now.)
EDIT (additional comment): Generally, the meaning of the "elliptical" から can vary depending on situation.
A different example from the one above:
もう、帰るから!
I'm leaving! (...so don't talk to me, because I'm angry, frustrated,
etc.)