No, no matter what, the first random heroic you do in a day rewards two Emblems of Frost (at least currently).

I think I saw somewhere that you can choose wich dungeons you wish to be looking for. So if you don't want Occ you can just take it of the list of dungeons you're looking for.
With this you should be able to avoid the situation you're discribing.

"Question:When is the particular dungeon determined and is it fixed if you degroup? Say you find yourself assigned Oculus and you have no desire to do that. If you degroup (taking the deserter debuff) and jump back into LFG 15 minutes later, are you locked into having Oculus once it has been assigned once even though you haven't completed it?
Blue Response: The dungeon is determined once the group is filled. If the group does not like the instance that's been selected, they can leave, get the Deserter debuff, and try again to get a different random dungeon once the 15-minute debuff dissipates."

"Question: You sort of answers this before, but if I got put in a dungeon that I -really- didn't want to do as my first random heroic of the day, and I drop group, wait the 15 minutes and join a new one, do I still get the 2 Frost Emblems? Or do I -have- to take the first random heroic that is presented to me to earn my Frost?
Blue Response: No, you will still be eligible for the daily loot even if you don't complete the first random Heroic dungeon you enter. "

This was taken from a Q&A, which can be found posted on MMO Champion here:
http://www.mmo-champion.com/news-2/queen-lana%27thel-icecrown-citadel-blue-posts/

Djbrill, although I can't say for sure, that's not the impression I got from this. If you could selectively eliminate dungeons from your "random" choice, then it's no longer random. You could simply eliminate all dungeons except the one you want to do. For the Random Daily, I believe it must be chosen from all possible dungeons. That's not to say you can't say "I want to group up for either UK, UP, or VH." but I don't think that would count towards the random dungeon. (Though, if you're letting it assign group members, they would count towards getting the Perky Pug.)

Again, I'm not 100% sure on this, so if there's anyone who's tried it on the PTR, maybe they would be kind enough to find out for us. =)

Random is random. You can do the random daily with either a PUG or a premade, but you get offered which dungeon when the group is ready and the button is hit.

You can leave the party if you get a dungeon you don't want, wait 15 minutes and try again, but it will still be a random dungeon. Possibly even the same one you refused last time.