For the most part, yes. Though they might not test you directly on an amino acid, you are most likely going to have to distinguish structures of amino acids, so I would be put that at the top of my list for things to memorize.
for the new MCAT, you sure do. I had several questions on my MCAT regarding AA structure, chemistry and naming. In addition, every student I've had since 2015 has reported similar.
Priority #1 side chain structure/property; full name
Priority #2 3 letter abbreviation
Priority #3 1 letter abbreviation
In reality, Priority 2/3 are right behind 1, and its not much extra effort so better to know it all. All evidence also shows that still not necessary to memorize is the Codon to AA table.