Usually, factory-resets do not touch the SD cards (neither internal and explicitly not external) unless there's an option to explicitly do so and one has checked that. In my experience (as far as I can remember from CWM) my cards were never touched. I'm currently using twrp where one has to explicitly check the corresponding boxes if one wishes to wipe them as well.
However, some vendors have configured that differently on some devices, including the internal SD card with the wipe by default. I don't think CWM adapted that on those devices then, but it cannot hurt to check.
If you backed up your phone to the external card, that backup should be safe there. However, you didn't tell what kind of backup you did. Talking about CWM, I assume you meant a nandroid backup1. As long as you additionally copied all content from the internal card to the external, you again should be safe. If not, it then depends on the "disk layout" of the ROM used whether it was covered with the "default Nandroid": if the card is just emulated from a directory located inside
/data using FUSE, it should be included with the
data.* backup. If it uses its own partition, it might not be covered (not sure if CWM gives an option to include it).
As it turned out in your case, the cards have been left untouched by the CWM-triggered factory reset as I had expected. But I'm not entirely sure if that's always guaranteed (though being the usual case). So it never hurts to "have a safety-net and a double bottom" ;)
1 Check our nandroid tag-wiki for details on that