No, the flight director pitch bar will command a 300fpm climb ONLY. There is no speed protection in V/S mode on the 757/767 unlike some other Boeing models. The autothrottle goes into "THR HLD" on takeoff (and then ARM if memory serves) which means that it is declutched and therefore you have full control over it. When you reach your altitude with "ALT CAP" the autothrottle will come back to life in SPD mode but by then you should have disarmed the autothrottle as per the engine failure checklist so it shouldn't be an issue. But, having said that, don't forget to reduce thrust manually when you level off or you will accelerate!
After takeoff with an engine failure the FD pitch bar will command a speed between V2 and V2+15 depending on what speed you were actually flying on liftoff, but when you press V/S this goes out the window. Later, when you select FLCH, pitch controls speed again.
I know, it can be confusing...