I'm going to go with answers: no and probably not, but maybe.
First, no, chips added to the bottom of Teensy 4.1 aren't ever accessed as EEPROM. They are used with LittleFS as a filesystem. Maybe that can be useful, but if you're expecting it to be used as the EEPROM library, that definitely will not happen no matter what chip to use.
So regarding whether this M95P16 chip can be used with LittleFS, I'm going to answer: probably not right out of the box, but maybe with some fiddling. There are 2 likely issues. The main problem is the clock speed. I believe we're using 88 MHz as the default, though there's been quite a bit of talk about wanting 132 MHz. This chip shows 3 maximum clock speeds on the first page, 50 and 80 MHz. If might be possible to use if you slow the clock, but the default clock will probably be too fast. There's also the small matter of editing LittleFS chip detection code to recognize this chip. That's probably doable with some fiddling, as I see it supports the JEDEC ID command (page 21, 37). You'd have to figure out what response it give and edit the table of known chips. Commands look like other chips, so odds are good it can work if you get the clock slow enough and get past detecting the hardware.