Hi. I don't want to spoil anything for myself so I haven't read the wikki about this. I just want to know if it's possible to complete the No Stone Unturned quest (the one with the Unusual Gems) without doing the main quest, and thereby not getting inside the Thalmore Embassy.

Thank you kindly.

If you got a patched game. Yes.
Patch 1.4 and upwards specifically.