Man, we have some smart Catholic cookies out there! I am duly impressed! I may have to relinquish authorship of this blog feature and let the rest of you write it. My little ol' answer may pale in comparison to the commenters' answers, but I am going to give it a whirl. (And be sure to check out the awards for blogger answers at the end.)
The answer: No!
The elaboration: Angels and humans are completely different creatures. Both are made in the image of God (possessing an intellect and will), but we are distinct creatures who cannot "turn into" one another.
Humans are body and spirit. Angels are pure spirits, without bodies, and are neither male nor female (though they can "appear" in bodily form for God's purposes). We humans are not complete without our bodies, which is the reason that death is so unnatural for us, as death separates the body and spirit. We were not created to be disembodied spirits like angels.
Those dying in friendship with God (i.e., dying in a state of grace) will enter Heaven, generally after a much needed purgation/cleansing.* Once in Heaven, we will be saints. So, it is correct to say that when people die and go to Heaven, they become saints, not angels.
Other interesting points: Angels are actually a higher order of creation than humans. Did you ever wonder why Lucifer and a third of the other angels rebelled against God before the creation of the world? Well, it is traditionally held that God had revealed to the angels His plan for His Son, and that Lucifer and his minions could not stand the thought of the Second Person of the Holy Trinity becoming a lowly human instead of an angel. Such a humiliating plan was too much for them to bear.
At the Final Judgement (which is the judgement at the end of time when Jesus Christ returns, as opposed to the Particular Judgement, which each soul receives upon his or her death), the souls of all humans will be reunited with their resurrected bodies. The souls in Heaven will have glorified, transfigured bodies (and that's a really cool topic for another time). We will be again as we should be: body and spirit.
Any personal being (angel or human) who is in Heaven can rightly be called a "saint" since the word itself means "holy" or "sanctified." This is why we can speak of St. Michael the Archangel, or St. Gabriel, or St. Raphael (all angels).
Some saints in Heaven are "canonized" saints, which means that they are given the special honor of an official feast day on the Church's calendar. The rest of the citizens of Heaven, i.e., the uncanonized saints, are celebrated on the Feast of All Saints.
Finally, the fact that we humans are only truly integrated when we are united body and soul is important. Many Protestant groups see the body as "less than" the spirit. To them, the body is seen almost as a necessary evil, shackling us until the day that we can be "released" from the body at death, our souls then "free." But how wrong this is! As Catholics, we know that God created humans as body and soul, and called it "good". Our Savior then deigned to become human Himself, taking on flesh. When He redeemed the fallen world by offering His human body on the Cross, He redeemed all bodies and all matter. The Incarnation (God becoming man) has implications in all we do as Catholics.
Oh, but you guys already knew all that! Sheesh! I am going to have to work a lot harder next time to stump you.
Now, for the awards:
The Brown-Noser Award (or, The Most Enthusiastic Respondent Award) goes to... Second Chances!
The St. Thomas Aquinas Award for Thoroughness of Doctrinal Explanations in a Small Comment Box goes to... Mrs. Mike!
The Greatest Publicly Revealed Past Humiliation Concerning the Subject of Angels and Humans Award goes to... Wheelbarrow Rider!
The Best Integration of Scripture AND a Frank Sheed Reference Award goes to... Lauren!
The Brevity is the Soul of Wit Award goes to... Beth, answering correctly with just nine words and an emoticon!
The Most Creative Use of a Cuss Word During a Doctrinal Discussion Award goes to... Sew! (Who was also the first to supply the correct answer, so she also receives The Quick on the Draw Award for Speed and Accuracy!)
The Best (Worst) Disguise of a Blogger Identity Award goes to... my daughter Cecily (can you figure out which comment was hers?)
And finally,
The Most Courageous Response by Admitting to Being Educated in the Public Schools Award goes to... This Cross I Embrace! (Just kidding -- I was a public school kid, too!)
Anyway, that was really hard, because you all deserve an award. You all got the answer RIGHT! Don't feel bad if you didn't get an award this time... It's my way of making sure you come back next time!
Tune in next time (well, sometime in the future) for the next installment of Doctrinal Quiz Show!
*The doctrine of Purgatory may be discussed in a future post.