I knew that adding a supplementary question was a bad mistake. Just in case the original question is overlooked:
Will my Electrical Engines still draw EU when my TE machines don't need any power? Currently I have them connected to wooden and gold conductive pipes, would Redstone Energy Conduits give a different answer?
From what I know, they will continue to draw EU. In fact, if the TE machines are full on power, the engines will start to fill and eventually blow up the conductive pipes. (This was a fairly recent change to Buildcraft which was made since the team noticed how TE conduits worked.)
As for the Conduits, they'll continue drawing power from the Engines, though they won't blow up, they just "delete" excess power. I'd suggest using Gates to shut off the Engines when all your TE machines are full.