I would have to ask you what you mean by prior training? Does that mean only certification?
If so, then yes, my buddy and I have certainly pushed the limits of our official training without becoming certified to the next level of training.
However, we also educated ourselves before doing so in order to fully understand which rules we were going to break and why, and what the possible consequences of those actions might be. We then took steps to minimize the risk to ourselves and prepare for those risks before making dives that were technically were not within our training limits. Also, there were a couple of instances where we had 'supervision' sort of. For example, we participated in some ocean diving with a charter that specifically stated that you must be advanced open water certified to make the dives. We called the DM and told him up front that we were not AOW, but that we were confident we could do the dives. He told us to come up a day earlier than the charter and dive with him, that he would assess our skills and make a decision. Then he let us do the dives, and to be quite honest, we were more proficient than the majority of AOW's on the charter.
I'm not going to tell you not to push your limits, though that would be the responsible thing to do, but I will tell you that even if 'formal' certification is not involved, do some reading, talk to some experienced people and prepare yourself before you do it. Then have a damn good time!