Not really tho. The progress is account wide but you can only hold the quest on one character at the time. And furthermore it's bugged if you try to switch it to another char by abandoning and picking it up again. Like i said, it just disappeared for me, now there's no Xenology quest anywhere for me and I've read from others complaining about it.

lmao, I hold it on all characters at once ahahah

Lol, what did you do for xur to be privileged like that? 😁