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I've learned that Etudes are performance pieces, but what about piano studies like Hanon and Czerny?

Well pretty much anything can be played as a performance piece but many of them would be very dull to listen to. Personally I find Hanon extremely boring and I believe many other people do too. Czerny less so but still there is not enough in most of them to make then sufficiently interesting for the listener in a concert setting.

Having said that there is a huge list of studies - usually called Etudes - by great composers which work well as performance pieces. All of Chopin's and Liszt's Etudes as well as much of Scriabin, Kapustin, Busoni and many others.

So to directly address your question. You can play anything as a performance piece but you will not attract many listeners if the piece is not intended for that purpose. "Etude" and "Study" are often used interchangeably so that is not the distinction you should use. It comes down to the quality of the music and it's usually obvious if a piece is just a mechanical exercise or a well-constructed and interesting-to-listen-to piece of music.

Hope that helps.

I have taken a few works from Czerny, slowed them down and played them as prelude pieces in church. One day a woman commented how gorgeous a piece was that I played and I told her it was by Czerny. She immediately called a meeting of the liturgy committee and had a bylaw drawn up stating that the organist shall NOT PLAY FINGER EXERCISES for worship and they presented me with a list of acceptable composers. That next Sunday, I played several of Bach's two part inventions. Bach was an acceptable composer. I didn't have the heart (or stupidity) to tell them that the choir anthem that week was written by an atheist (Rutter).

I will be playing a concert on a theater organ this June and am deliberating playing a Czerny piece because it sounds really cool with the xylophone and bell stops.

The word etude means study. Most were composed for specific techniques formerly on harpsichord, then, when piano made its debut, for all the new techniques that were available. Czerny, Cramer, Bertini were prolific for the piano, Kreutzer and Rode for violin.

Chopin and Debussy took this writing to a different level, with their Etudes de Concert, and Liszt went even further, both in difficulty and Romantic quality. The latter ones, I guess would be ripe for performance. Although earlier ones were specifically for learning techniques, which is what studies are for, after all, any could be and have been used as performance pieces. It rather depends on the player and the audience.

Hanon and Czerny could well feature if one wanted to show particular facets of playing prowess to a selected audience - or could be segued into an interesting pastiche.

EDIT: not certain, but dynamics probably don't play a great part in studies. However, applying some of your own would perhaps make them much more like performances.

The short answer is yes, it can.

A better question is "Is this a good idea?", and only you can answer that. Try recording yourself playing the study and listen back to it, perhaps back-to-back with some other piano music you enjoy listening to. If you find it horribly dull, or much less enjoyable than the others, perhaps don't play it as part of a performance.

Anecdotally, one exception of a composition as a drill for a guitar master (so I am told) was designed for drills and mastery of
the concert guitar solo work "Recuerdos de la Alhambra" by Francisco Tàrrega. Transposition to piano would take the skill of Art Tatum.