I did something similar, when I moved server to another datacenter, and I wanted to have min. downtime. In my scenario I had two hardware identical server, so I remove one of the raid disk from working server and add it to identical server, and later re-add second disk.
First be sure, that you have grub installed on both drives. Here is described how to do that.
Now you can power down your machine and remove one of the disk.
On the second one you do upgrades. If it works, delete partitionson the removed drive and poke it back to raid.
If upgrades mess up your server, simpy swap drives, delete partition on messed up disk, delete partitions and add it to raid.
Best way to do that is here