Now there's an interesting take, and clarifies the position I personally hold on the issue. I doubt He would take it because He would know He wasn't getting sick. There were promises associated with walking in the will of God that stipulated that they would not get sick, but that if they rebelled against Him they would (Deuteronomy 28); granted, they might get the common cold or sniffles, but they would not be succumbing to leprosy or some of the more serious illnesses of the day.
Trouble is, you have a lot of Christians that don't actually walk that close to the Lord like they're supposed to, which makes teaching this view rather complicated. You don't want to make someone feel guilty about taking immunization shots if they are not in a place of walking close enough to God where they can stand in faith against illness, knowing it does not have dominion over them in Christ.
So yes, He likely would not have needed or taken vaccine shots. Just not sure it's a doctrinal position you can force upon all Christians.