Not if you haven't gone into device manager and set both drives to run in Performance Mode with write caching enabled. If you haven't nothing will happen because the sole purpose of that icon is to flush the write cache for devices that have it enabled and are plugged into a non-internal bus (USB/firewire etc).
Even with write cache enabled I yank my drive out all the time because that damn icon never works, and I still never get any data loss.
The way to make sure the filesystem is fine is run this in CMD
Of course if you REALLY want to be sure and are fine leaving it overnight (depending on drive size and speed) run this