Was Crocodile stronger at Marineford? Or was he holding back in Alabasta?

 During the Alabasta arc, Crocodile displayed a level of power that was initially considered overwhelming by the Straw Hat Pirates. He possessed the Logia-type Devil Fruit called the Suna Suna no Mi (Sand-Sand Fruit), which granted him the ability to control and transform into sand. He had a reputation as a Shichibukai and controlled the desert kingdom of Alabasta from the shadows. His strength was showcased through his battles with Luffy and others. At Marineford, Crocodile was present as part of the war that took place at Marine Headquarters. While he did participate in the battle, he didn't display the same level of dominance as some other powerful characters present. This has led fans to speculate that he might not have been as strong as initially portrayed in Alabasta. It's important to note that power scaling and character abilities can be subject to interpretation and development by the author. Oda often keeps details deliberately open-ended to keep the story intriguing.

Could we catch up with the current state of technology fast enough just from the documented knowledge in some kind of extreme event like a war breaking on grounds where most of the worlds peak technology is produced like Taiwan?

 It is not possible to accurately predict what would happen in the event of a hypothetical extreme event like the one you described. However, it is unlikely that a sudden and significant increase in the pace of technological development could be achieved solely through the documented knowledge that exists at the present time.

There are several reasons why it might be difficult to catch up with the current state of technology in the event of an extreme event:

Knowledge gaps: Even if all of the documented knowledge on a particular subject were to become available, it is likely that there would be significant gaps in understanding that would need to be filled in order to fully comprehend and replicate certain technologies.

Lack of resources: Developing new technologies often requires access to specialized resources and equipment, which might not be readily available in the event of an extreme event.

Time and effort: Developing new technologies can be a time-consuming and resource-intensive process, and it is unlikely that sufficient progress could be made in a short period of time, especially in the face of other pressing concerns such as the aftermath of a war.

Unforeseen challenges: There is always the possibility that unforeseen challenges or setbacks could arise when attempting to develop new technologies, which could further delay progress.

In summary, while it is possible that some progress could be made in catching up with the current state of technology in the event of an extreme event, it is likely that this process would be slow and would require significant effort and resources.