I have to use a VPN to access it, so I usually don't bother
Yeah, Callen knows that ultimately, what Arkady thinks doesn't really matter. The only person, other than him, that gets a say is Anna.
I didn't get the impression he was against marriage, from what he said, but he definitely seems to have accepted that marriage isn't something he could see Anna wanting. If it's what she wanted, I couldn't see him objecting.
That could be it. He's thinking about it, and decides at the end of the episode to go and ask. Maybe doesn't want to give himself time to rethink it again
At least it wouldn't be a life/death cliffhanger.