No, I just upgraded a CO ticket using NW miles 20k one-way for HNL-GUM-NRT-SIN including the NW codeshare flight (all considered one upgrade). In fact, if I didn't have a layover in HNL, I would of been able to upgrade the whole thing for 25k (though IAH-HNL was unavailable for upgrade anyway). As long as all your legs are in the right fare class and seats are available in R, Z or F (that's what agent told me they come out of), should be ok. Just call NW to request the award and they will handle the rest.
In fact, I really have to thank you for your post. I just assumed that for a CO purchased ticket, I would need to use CO miles and was waiting for enough to post to request the upgrade. You inspired me to call NW and sure enough it was done!, thanks