No Berry, they are not accurate, compared to most other service rifle's. Anything past 300m's is a severe challenge for an AK-47, even in the hands of the best user, whereas, the Australian Army with the Steyr AUG, 300m's is the basic qualification range for ALL soldiers, not just riflemen...
The design features that allow for the AK's justifiably famous "ruggedness" are the same features that minimise it's accuracy. The weight of the rifle has almost nothing to do with the accuracy of the rifle. An AK-47 (or any rifle for that matter) will be more accurate when firing single aimed shots, than when firing in automatic mode, however the AK-47 has proved demonstrably inferior to other in service mil-spec rifles over many years.
AK's were designed for poorly trained conscript armies where weight of fire was more important than descriminate accurate fire. Accuracy was sacrificed for simplicity and in the context of conscript based Soviet Era armies, is a fine rifle. It is not a rifle one (ie: me) would choose for accurate shooting however. Even the Soviets didn't use it for this purpose...