Yes and No. The ST-16 knows or reads the current version. So if you try to re-install the same version it'll tell you the firmware is current or up to date. So you can try it and it'll let you know...
Now if you feel you "need" to reinstall the current version, I "think" you need install a certain version thats like 2 or 3 versions old and start re-applying the upgrades till you get to the current version. There is a thread about how to do this. I don't recall it at the moment...