You forget that Labour has already used the electoral college while in government in the meaningless six-horse race election of Harriet Harman as deputy leader after the Blair/Prescott resignation in 2007.
Yes, it is constitutionally the case that the affiliated trade unions and Labour Party members could take control of the party they created and own and ignore the power of the business interests which have bankrolled and controlled New Labour. But sadly that power is only a theoretical one. Why?
First, there is nobody in the New Labour government who has the slightest loyalty to the trade union movement. Mandelson et al would leave the party before they became representatives of ordinary working people.
Second, the trade union leaders lead hollow armies. Just as they have no friends above they have no active rank and file below them. Any attempt by these men to exercise their power would just show they had none. Much more likely in a leadership contest, the trade union leaders would be there to be bought off by the competing candidates emerging from within the upper echelons of New Labour.