If you're not rated on a machine, and it's not a training flight, then you have no formal role in the cockpit and can't log hours. From the point of view of a regulator you are just another passenger, and must be briefed and treated as such by the commander.
However you can gain extremely valuable experience of operations in more complex types by sitting in a spare front seat, and there is no bar to you doing so.
Do be careful about the requirements for and the boundaries between public transport flights and private flights though. Check the operator's manuals and local legislation carefully to make sure you are on the right side of the law. For example in EASA land there is nothing wrong with you handling a machine on a private flight under the supervision of an appropriately qualified commander. You might think that would allow you to gain experience, but flights for an Air Operator are often defined as public transport (ie not private) even when there are no passengers (eg. positioning).