Does Soldering and Attaching/Using Molex Connectors reduce power draw?
It's not clear without a diagram what you are actually asking, but most likely, no, it doesn't work that way.

Think about it.  If a connector in series would reduce power consumption, then why do appliances draw any power when plugged into the wall as apposed to wired directly?  What about using extension cords?  Shouldn't those allow for free power?

Regardless of any electronics knowledge, basic high school physics says you don't get free power.  Running a fan while the power source isn't putting out power violates this very basic rule of physics.

Even worse, since no connector is perfect, there will be some power dissipation in the connector.  That means the ultimate load gets less power, or the power source ends up putting out more to compensate.  Again, there is no free power.