Is it possible to retain the created/modified/accessed dates of a folder when...

[Megalith]

...you're overwriting it with a folder that has the same file name? I guess the setting I'm looking for is "Do not replace original folder if being overwritten with one that has the same file name."

[admin]

Not possible without scripting. On Custom Copy with "Preserve all item dates" all three dates are copied from the source to the target, and without "Preserve all item dates" the Modified and Accessed date in the target are updated to now.

You could do it with scripting using SC filetime to get the current dates, then copy the folders, and the SC timestamp to reset the dates to the original ones.