Using only the physical media, yes sure why not. It's been done often enough with RJ45 plugs which should offer similar performance for I2S and easier to use, but with an HDMI plug I was hoping to see the additional signals like the CEC bus being used for comms or so. I built an external DAC with an LVDS input with a RJ45 plug 10 years ago and it worked great.
Electrical LVDS (not the protocol which is a bit more) doesn't care about the physical cable as long as it's a 100R differential pair so you can use whatever plug of choice, be it HDMI or DisplayPort or whatever. These cables are capable of higher bandwidth than CAT5e/CAT6, but for I2S there should not really be any difference. CAT7 is a nice option since the cable is not only shielded but every pair is shielded too.