Will (LiPo) batteries draw current/voltage between packs if main lead is disconnected?
With just the batteries? Nope. Current can only flow if the loop is closed.

BUT!

With LiPo batteries there is often a control board, they will at least still use a tiny amount of power (in the order of micro amperes usually). Some more advanced technologies can actually actively balance cells while in use or while charging, Linear had a nice chip that does that. In such a case a little while after you switch it off, it may keep currents flowing around between the batteries to balance them for a tiny while after. But those packs will be very rare.

So simply put: If there's electronics in there, anything could be happening, if there isn't, then loop broken means no current anywhere, ever. Although with LiPo it's very smart to have electronics at least for per-cell protection.

(Except for a battery's inherent self-discharge, but that's a current that flows inside each cell, so that still doesn't affect other cells in the chain and that is extremely low for Lithium types.)