How much can Apple keep this from the public eye? Up until release, or up until announcement?
I'll start backwards. For many devices, you can go to an outside company, certified by the FCC as their proxy. Unlike the FCC proper, they don't have to say anything right away. In other words, you can get your approval and keep it hidden as long as you want. The moment you want to sell, you have the outside company give the FCC the approved submittal and it becomes public.
However, cell phones are in a special category, and you can give your test paperwork only to the FCC. (Since it can cost tens of thousands of dollars to run tests, you don't do this unless you're pretty darned sure you'll pass.)
At the time of submittal, things are still private. The FCC checks the results, ask privately for any clarification, and you go back and forth like that until they stamp an approval on it. At that moment the approval becomes public knowledge, or at least can be found if someone is watching.
But... you can add a request to keep the parts list, schematic, manuals and any photos (such as the test setup) private for a longer time. I believe it only costs about $300 to do this, but don't quote me on it. You can also request that the schematic and internal details be kept secret forever, so that others cannot make direct copies. Apple does this a lot.
In the case of a privacy request, all you can see are the radio test results. That's enough to know if it's 3G or not, but not much else.
Here's the thing. We all know 3G is coming, so even if one were approved, so what? It wouldn't be a surprise. It wouldn't tell us when it's going on sale, what it looks like, does it have an 800x480 screen, 32GB, keyboard, etc.
So in theory, they could wait until the day of approval and announce it. Or announce it weeks later. But that lacks the showmanship that Jobs likes. So your guess is as good as mine, as to what they'll do. I'm sure there are long time Apple watchers around here who can give us a good guess.