No, it wasn't swirling around. I kept seeing 1s (above the ramp leading further down) in my tunnel one z-level BELOW sea level. Below that was 7s. Still, I'll have to try it again later.
Edit: I tried it again, but the ocean on my embark site was only two z-levels deep (and most of it was only one z-level). I should have looked for deeper. However, the water entered the aquifer from below, and it still instantly drained the top z-level where the water was two z-levels deep. Due to the small amount of water drained, I didn't notice the slowdown when it happened. I'll try to get more conclusive results next try.
Edit 2: I'm trying with a deeper ocean. I dug a ramp 2 z-levels below an aquifer such that it started leaking water, then I sacrificed a miner to pierce the ocean from below with another ramp. ...my CPU is still working on this. I don't think that miner has even died yet. I supose I can't get anything really conclusive out of this until it finally works through all that water so I can see it myself.
I think it's working, though, since when I alt-tabbed to DF and the window finally showed up, I saw a bright blue 7, a dark blue 7, and a period representing open space right next to each other, suggesting serious drainage.
Edit 3: It's still going, but now I've lost the entire top z-level of the ocean, and there is most definitely not that much mined out down there. I believe it's safe to conclude that you CAN, in fact, drain the ocean upward into the bottom of an aquifer. And what I saw in my first experiment? It was what an infinite source of unpressurized water being drained into an infinite capacity drain SHOULD look like.
Edit 4: ...wait, crud. I found something that invalidated my experiment. I screwed up. Time to try AGAIN.
Edit 5: Okay, I tried it again elsewhere, this time making sure that the aquifer was not channeled from above in the same tunnel where the ocean flows in. The aquifer is on the same z-level as the lowest z-level of ocean. I dug a ramp under the aquifer so that it would leak, then I sacrificed a miner to dig a ramp under the ocean. The ocean flooded the tunnel immediately, but it did not drain. That's probably as expected. Then I dug a channel into the aquifer from above, making sure that the ocean water had no way to reach it from above this time.
I then engineered a single floor tile cave-in above this channel to knock out the floor below the aquifer that I couldn't get to (but which it was leaking through). When I had a dwarf pull the lever to trigger the cave-in, the game ground to a halt for a while, and when it allowed me to pause and look around, the ocean had begun draining as it did in the struck-out section above (where I did something stupid). Therefore, an ocean CAN be drained into an aquifer from below, provided you also have access to the top of the aquifer and said aquifer is only one z-level thick (not counting the leaky z-level below it).