Can dopus help me do the equivalent of a DOS Replace command

ie, do a find command to find all files matching certain criteria, and then replace them by a single file (that I might have copied into the clipboard, for instance, or might have selected in a LHS Lister)?

Not as a single operation. You could do the find part and then copy the list of filepaths to the clipboard to paste into a command which copies the file to each path.

Whether that's good enough depends on how often you need to do it, I guess.