No, do NOT do this. This just gives a boundary to the left and none to the right of the Democratic Party.
Always vote for "progressives" (or ideally socialists) in the primary. If you're in a red state, consider even voting and running in the GOP primary instead.
If your candidate loses the primary, VOTE AGAINST THE PARTY IN THE GENERAL. Make it apparent that they either move to the left, or they lose.
And - crucially - join and form organizations that publicly state they will do exactly this.