Yes the EEC protects against overspeed,doesnt mean firewalling like your life would depend it,an overspeed would not occurr.
Max thrust by firewalling with eec ON would result in over thrust.
As written above not an issue..but best not do it unless dictated by few conditions(windshear/terrain).
I believe CFM on the 737NG have been tested to mac temp plus 40 deg C for 5 mins without need for maintenance.
Nevertheless,care of your engines and theyll care of you.