That said, they didn't even use test mode when I took the SAT, so I don't know.
I would actually take it a step further and say that graphing calculators aren't even that useful in instruction, especially now that students all have computers and can run Desmos, MatLab, or whatever. I had a TI-86 in high school, and the only class in which I found it indispensable was A.P. Statistics. Maybe I'm being narrow-minded, but I always thought those things were a bit silly and gimmicky and sort of resented that my parents had to buy me one for school.
I hated it while in school, but retrospectively i think it was a pretty good idea actually :)
Ideally it would be an SD-card plugged in at the top edge of the calculator. The area around that connector could be clear plastic, with visible circuit traces running to the CPU.
Of course it is always possible to fully replicate the calculator. I'm sure there is a Chinese factory that could do it. Stopping a trademark violation like that is the job of the port inspection and customs enforcement people. The situation becomes like illegal drugs, but with much lower demand and much more difficult production.
Simply replacing the chip is some serious electronics work. These aren't socketed DIP chips. They aren't even BGA. TI puts the bare naked silicon chip right on the board, bonds wires from it to the board, and then covers it with a blob of black glue.
My suggestion of clear plastic makes this even harder. Modifications would need to look normal. The part of the board between the SD card socket and the CPU should have a minimum of clutter and a colorful boarder box, making it easy to see where one should look for modifications.
The Ti83 is how I learned to program.