Welcome to the forum!
On a std yes, It will update if needed, on firmware updates I had found a quirk (kind of fine print) that when the firmware said it was completed, we would power everything off. But actually what I am getting at, is maybe your supposed to power off the phantom, leave the remote on, then power the phantom back on to complete the update.
I personally refuse to do any more firmware updates, some have problems, some due, my experience was twice I ended up sending my Phantom and the remote in after a firmware update. Even after it said it was successful on the first try.
Rod