Are the Ethernet frame checksums even visible to Wireshark, which hooks into the IP layer? would some of the ethernet stuff be only visible within the ethernet card itself, not to the software stack?
Sometimes they are. It depends on how the capture was generated. If you look in the options of Wireshark there is one to detect bad checksums, so clearly there is a way to capture them. Here is one such way: https://stackoverflow.com/questions/22101650/how-can-i-recei...
This can be used to detect partially-bad network cables, because there is no reason you should ever receive a bad FCS.