Can a non-catholic receive the Sacrament of the Sick and reap its benefits?
Eastern Orthodox may request the sacrament and receive it at pretty much any time:
Canon 844 §3. Catholic ministers administer the sacraments of penance, Eucharist, and anointing of the sick licitly to members of Eastern Churches which do not have full communion with the Catholic Church if they seek such on their own accord and are properly disposed. This is also valid for members of other Churches which in the judgment of the Apostolic See are in the same condition in regard to the sacraments as these Eastern Churches.
Christians from other backgrounds usually need to be in danger of death, share the Catholic faith of the sacrament, be unable to obtain their own minister, and request a Catholic priest:
Canon 844 §4. If the danger of death is present or if, in the judgment of the diocesan bishop or conference of bishops, some other grave necessity urges it, Catholic ministers administer these same sacraments licitly also to other Christians not having full communion with the Catholic Church, who cannot approach a minister of their own community and who seek such on their own accord, provided that they manifest Catholic faith in respect to these sacraments and are properly disposed.