I remember separately providing .idat files for at least one project (outside of GEO). While the detection p-values may be helpful for filtering certain probes in certain samples, I think they should have provided percent methylation / beta values (although in that particular project, I think the GEO format did request separated signal and detection p-values).

However, I can see some more recent 450k datasets where you could download .idat files in a GEO supplemental .tar file, so you could try contacting the authors about those files.

You can also update GEO submissions, so I will ask about updating the .idat files for the dataset that I am thinking of, and provide an updated comment. However, you may end up finding a solution for this particular dataset sooner by contacting the corresponding author (and/or by calculating the percent methylation from the separate methylated and unmethylated signals; you have to make sure you don't divide by zero, but one explanation for the beta value is provided here).