I used a vacuum cleaner before, now I have a small hobby compressor (meant for painting plastic models) and an unused small paint gun as trigger. So far I have spun every fan available at full speed during the cleaning process. Vacuum cleaner made them really whine, I guess that has to stop now in light of this new information.
Depending on the motherboard design, you might be able to get away with it if zener diodes were implemented on the power feed to the fan.
Without knowing if they are, it is a gamble to run the fans with air. Of course, it is also possible for the fans to have zener diodes installed in them as well.
Easy way find out is to take a volt meter and connect it to the leads of the fan then run the fan. Set the volt meter to 5V range.