Yep. "Greek is gendered, the gender is embedded into the words". Sure, but I can speak whole normal sentences without referring to gender at all, something like "went to the supermarket and bought x y z, then did a, b and c and came back".
You can talk about someone at length without mentioning their gender once.
This is absolutely true, but sooner or later you’ll have to pick a gender or you’ll just end up sounding funny at best.
language 2 embeds gender in the word itself.
names are words.
it's a lose-lose situation: native speakers of language 2 will look at what you wrote and cringe or just assume you're ignorant. they won't get the point you're trying to make, null, nada, 0% chance. source: i'm a native speaker of language 2.