Even though it may not be specific to the EFTO case the OP had in mind, Compressor stall and flarepilot raise a very relevant point, especially in relation to the larger jet engines in pre-FADEC days.
No two engines would accelerate (or decelerate) at exactly the same rate, and IIRC there was (and is?) a certification allowance of about 8 seconds (?) from idle to what is often called TOGA thrust on jet engines. In my limited experience (Conway, Spey, JT3D, CF6), the worse by far was the JT3D as installed on the B707, on which the asymmetry potential is obviously greater than on an a/c with tail-mounted engines.
This differential spool-up time could even catch you out on the B707 if you selected cruise thrust hurriedly after a descent at idle (amusing yaws followed). Most of the delay was in getting the engine to accelerate from idle to the sort of thrust you would use on the approach (about 1.2 EPR). After that, the thrust increase was rapid.
Turning on to the runway centreline for a rolling T/O (standard Boeing technique), the handling pilot "stood-up" the thrust levers for a target of about 1.2 EPR, The F/E monitored the engine acceleration and tweeked one or more levers if necessary. When satisfied that they had all spooled up, he announced "stable", whereupon the pilot advanced them to somewhere just short of where he guessed TOGA would be achieved. Being already spooled up, asymmetry was not normally a problem. (Of course, being an American engine, the thrust-levers could not be pushed fully forward; the F/E had to take over again and modulate the EPRs.)
There was significant potential for a runway excursion if an outboard engine failed during engine acceleration (before the rudder became effective), particularly on a wet runway.
My GUESS (!) is that the Allison turboprop engines on the Herc are already "spooled-up" before the take-off sequence begins, so most of the increase in thrust is achieved by coarsening the airscrew?
As an afterthought to an already long-winded post, I'm not sure how much experience the new generation of jet pilots get in using differential brakes to keep an a/c on the runway on the rare occasions that may be necessary, as vilas has pointed out. On the Dak, it was a vital, everyday tool...