The SPOT should work fine. Be sure to read and understand the manual before you go. Give everyone the link to your shared page so they can actually follow you. Have an understanding when you will send which messages.
I have a SPOT 2, which works better than SPOT 1. My profile has a link to my shared page. Sometimes it has something interesting, and sometimes it doesn't. I send "custom" from summits, "OK" when I get to camp or a trailhead, and "track" when I'm moving. I turn it off when I'm driving or at a camp.
BTW, cell phones coverage is hit or miss on Whitney. It'll probably work from the summit, but won’t work reliably anywhere else.