I had the great honor of being an "extraordinary minister of the Holy Eucharist years ago when Pope John Paul II came to the United States. This was before I became a deacon in 1991. There were about 500,000 to 700,000 + people at this mass. We (the Eucharistic ministers) were all given a ceramic ciborium (I acknowledge that now, them must be of a precious metal) and I was about 175 feet from the altar where the Pope was saying mass. We were instructed to then proceed to different stations where we distributed Holy Communion. So, no, the hosts do not have to be on the altar to be consecrated. All that is necessary is for the intention of the celebrant to consecrate, in this case the Pope. We were allowed to keep these ciborium as a memento of the mass. Mine is kept in a special place in my home.
Deacon Ed B