Will electrons be taken from a metal plate if a positive charge is applied to it?
Maybe a handful, but definitely not enough to do anything besides equalize the potential (voltage) between the two. 

Basically, the only thing that happens is charge balance occurs and the voltage becomes the same between the battery's terminal and the plate. 

An extreme example of this is when helicopters hook themselves to the high voltage power lines. There's actually a considerable amount of electrons flowing, but it's not harmful and it's only temporary until the potential is balanced. In this case, the battery is the power line and the plate is the helicopter.