If one was sat their feet back, doing anything but being close to the controls and both AP's went on strike together at the same time.....yes there would be a diversion from straight and level no doubt.
If you were feet and hands on the controls when that happened.....yes....the diversion would occur.
How big the diversion would depend upon the reaction time of the Pilot "flying" the machine be it by buttons or by human appendages.
Add a complete and instantaneous loss of AP's and everything but standby/emergency instruments.....it would get interesting.
To be IMC when it happened....would be really interesting.
Add night time to it and Holy Mackerel Batman!
I recall the good old days when Air Log sent their brand new 76A's offshore to earn revenue until they could be sent for installation of the Sperry Kit....and those were not good ol' days.
I also recall a Bell 212 Operator that did not think SAS/AP were needed for night offshore flying citing "But, Gee....it is VMC weather minimums we are using.". Never mind the absence of surface lighting or horizon.
This 76 Crew rose to the occasion and did an excellent job and deserve accolades for their performance under what must have been very stressful conditions.