I believe that concern is answered in the post.

"When a new tier of raiding gear is released or a new PvP season begins, your higher tier of points will be converted into the lower tier. For instance, if a new tier of raid gear is released, your Valor points will be converted to Hero points, and similarly if a new PvP season begins your Conquest points will be converted to Honor points. Of course that means with these new releases you'll always begin without any of the higher tier of points, and thus be unable to stockpile them."

Sounds like it's an automatic thing.

I read that, but that is not what I meant. For example, when ICC was released, I knew that I wouldn't be able to get in there for a very long time. Therefore, when I realized I only needed two more emblems to get a shiny piece of t9 I downgraded a pair of Emblems of Frost to Triumph so I could have the gear in time for my raid. I was wondering if exchanges like this would be possible under the new system.

I don't think it is ever a good idea to downgrade, because the older bosses and any randoms after the first "daily" will reward the lower tier badges (or in the new system, "points"). Just think about this: if instead of buying 2 triumph badges from 2 frost badges, you got a healer and a tank friend to run two bosses in a heroic instance. Boom, 2 triumph emblems, minimal effort. Because you had mostly t9 you outgear it anyway, and now you are not an ENTIRE DAY behind on your frost emblems.

Really, it's a matter of patience. If you really aren't interested in getting your highest tier gear as quickly as you are able, then it seems like running some casual lower-reward instances are better for you anyway. I've never traded down frost for triumph, because the time investment for frost emblems is so much greater than pugging 4 people to run a random OR just go blitz Flame Leviathan for some easy quick badges.