No, but that’s not a bad thing. People are people and angels are angels. They are different beings and should not be put in the same category.
In a simple manner, a person, after death in this world, is a person. The person retains his/her identity in the sense that the soul lives on until it is reunited with a physical body at the future time of resurrection. A person receives a reward in the afterlife based on whether the person freely chose “good” or “bad” in the challenges of life in this world. An angel, although also a creation of God, has no free will to choose good or bad, but is merely a messenger to do God’s bidding, and therefore has no afterlife per se.
The Hebrew word for "angel" is “malach.” The word "malach" is related to the word "melacha," which means “task.” Hence, a malach is an agent or vehicle which accomplishes a task. The English word "angel" comes from the Greek word "angelos" meaning "messenger" or "agent."
Angels come in all “flavors”. The ones we may be most familiar with nowadays are the ones that accompany us home on Shabbat. On Friday night we traditionally sing, “Shalom Aleichem, malachei hasharet, malachei Elyon, mi’Melech malchei hamalachim Hakadosh Baruch Hu… — “Welcome, administering angels, angels from Above; from the King of the kings of kings, the Holy One, blessed be He…”
Having said all this, if a person refers to another person as “an angel” I would not object to this terminology, whether the person spoken about is alive or not. I would interpret the intent of the speaker as referring to the other person as an “agent”, so to speak, who does (or did) the good deeds of God in this world.
