No that was not the reason for installing the autopilot. However it was observed by a british test pilot post-war though that the aircraft would have been exhausting to fly without one.
How you can be so sure of the 152s handling I do not know, few people flew it and none are still alive today afaik. The reason for these stability issues were the MW-50 70 liter tank behind the cockpit, it was added and not part of the original design. There were also many versions of the 152 discussed and worked on, we have only one of these in AH and people forget there were the A/B types, the E and C and the H which is what we have. So which one was stable you say? The C version had the 70 liter tank removed and one of the inner (left wing) 140 liter fuel tanks were used for MW50 instead, this was forced because of the situation on the ground which saw US troops overrun the facility manufacturing this sub assembly.
The 152A/B had finished prototype testing and were dismissed by the RLM as early as Oct '43. These were meant to be powered by the Jumo 213 like the Dora and the only difference between them basically was the 0.5 m longer wing span of the (short winged) 152, the familiar 152 wooden tail assembly and the much heavier armament. These were perfectly stable.
The H which we have in game is perfectly stable in certain load configurations. It just requires more knowledge to fly it well and I guess some give up on it before giving it a honest chance.
