I've seen quite a few people use J-1 or F-1 visas to enter the US. The kiosk is unable to admit us because of the I-20/DS-2019 check (and I believe the CBP officer needs to query SEVIS to check our status), so we always get an X - that just means you present your documents and receipt to an immigration officer. However all the travellers I know aren't Canadian. As non-Canadians we have paper Visas, which need to be scanned at a GE office before the kiosk lists the Visa - I don't know how that process works for Canadians since I believe you don't get a paper Visa.

Overall it probably doesn't matter if GOES doesn't know about your Visa, since we have to get processed manually regardless (i.e. the GE kiosk only identifies that we're GE/Nexus members and gives you a receipt to prove it, and you get an X regardless of choosing "Other" or "F-1"/"J-1"), but I'm not in a position to test that theory.

I've only ever used GE at YYZ, but the process there was similar to any US airport: kiosk let me select the Visa, and gives me an X, since YYZ is special you then look for the GE/ABTC/Diplomat lane (usually there are immigration officers closer to the machines in US airports), and a CBP officer processes your entry manually just like anywhere else.

I did end up in secondary once when using GE: that seemed to be a software glitch since the first officer couldn't admit me using their computer - the officers in secondary basically prioritised processing my passport and let me out after a few minutes without asking any questions or even speaking to me.