I tried this... once.
I wasn't worried about the gravity, I just wanted a handy way to get temp readings from inside my cooler.
It was long enough ago that I can't remember exactly how it went, but can remember that I didn't bother to try it a second time. If I remember correctly, the temps were changing amd spiking with pretty wild variance, to the point that it didn't provide any useful info.
No ill effects to the tilt, though.
P.S. - it didn't have similar spikes or variances in normal temp wort, or when dropping down to cold crashing.
P.P.S. - i don't think there is harm in trying, personally. But in the 1-2 years and 20 batches since I tried this, I think there are several better options, depending on your process. Nothing wrong with a decent instant-read thermometer and a refractometer. I bought fairly inexpensive refractometer... works well with a few drops of wort. And it is worth shelling out $$$ for a good thermapen... as you'll clearly want to use it for all the barbeque you should make to accompany your homebrew!