No, there’s no way to make saving in .doc format automatic.
If you save a copy of your document as .doc, Pages will still prompt you to save it as a Pages document the next time you open it. When you try to save it, you’ll have to click “Save copy as Word document” and you’ll have to overwrite your original file. You’ll even get a warning that asks whether you’re sure you want to replace the original.
To make matters worse, on my system I get a document import warning when opening some .doc files that were originally saved by Pages itself.
If you only need to share them with Word users once in a while (or after you’re done working with them), then the Pages export is fine. But if people need access to your documents all the time and you need to save them as .doc, it’s going to be a hassle to use Pages. Plus, you’ll have the odd case where your formatting or fonts or whatever get messed up by switching back and forth between formats. It would be great to have a universal document format, but that just doesn’t exist yet.