I had a good Obtain Diamond run that was structureless, but I didn't realize at the time that I needed to have them turned off. I was watching the first place Obtain Emerald No Structures run and they did the same thing. Would my run still be accepted despite this?

Its accepted as structure less (its fine) unless if you had a structure.

that's good to hear. Sadly, I didn't know about the rules in this community when I ran it so I deleted the world without getting the seed :/

theres a slight chance of it getting accepted though...