"The Avatar State is a defense mechanism, designed to empower you with the skills and knowledge of all the past Avatars." On screen we've only ever seen the avatar state used for bending related purposes but does it also transfer more mundane skills? Say Aang needed to put up a shelf but had never touched a screw in his life could he quickly enter the avatar state and draw upon all the D.I.Y. knowledge of all the avatars and assemble said shelf? (Ignoring the almost sacreligious nature of doing so)
Unclear, but also yes.
We never see Aang doing much besides bending whenever he's in the Avatar State. However, if your question is whether he has any kind of access to the knowledge of his past lives, the answer is a definite "yes". There are multiple instances of Aang accessing knowledge from his past lives that he himself didn't have.
Could possibly have involved the Avatar State:
Channeling Avatar Roku in Jeong-Jeong's tent, during which Aang-Roku states "I have mastered the elements a thousand times over a thousand lifetimes." Note that Aang seemed to have no memory of the exchange afterward.
Channeling Avatar Kyoshi in Chin Village, during which Aang-Kyoshi admits "I killed Chin the Conqueror." Note that Aang definitely had no memory of the exchange afterward.
Didn't involved the Avatar State, but would be a better way of building that shelf anyway:
Learning from Avatar Roku the details of his history with Fire Lord Sozin
Learning from Avatar Kuruk the details (well, some of them) of his history with Ko
Identifying the statue of Avatar Roku at the Southern Air Temple, before admitting "I'm not sure [how I know]-- I just know it somehow."
...or really just asking anyone in the Spirit World if they know