Is there a risk of runway excursion even though the throttle(s) in twin/quad are closed after engine failure ? (based on your experience: sim or real engine failure)
Yes. If you're at slow speed on a surface with a low braking coefficient and suffer an engine failure with rapid thrust decay. Practiced this a few times in the sim but luckily not for real.
Even pre-briefed as a training exercise, we ended up fairly sideways but still on the runway. Made my list of "things to think about" before taking off.
You're probably at the most vulnerable just as the engines reach T/O thrust, which will likely be full power if there's contamination causing the lack of braking action. Chopping the other engine(s) in a timely manner appears to be key, otherwise an exit stage left/right is on the cards. Reverse deployment helps and you can attempt differential braking but if it's really slippery, that's not going to do much.