Given the fact that we can have Kowalski on analysis and Private on recon, this is a piece of cake. With billions of dollars to grease the wheels of bureaucracy, foreign or otherwise, they should have no problem extracting whatever information they need from the required sources. Adding an imperial fuck-ton of drones to the mix should speed things along a bit, so should be found within 48 hours. That gives them another 24 to kill Bin Laden.
I think Rico's storage is worth mentioning a little. He hasn't shown a lot of limitation in the movies. In fact, other than being unable to speak clearly, they don't really show us his storage limits. He seems to never eat anything that he coughs up (although he probably is at some point?) and yet can produce a lit explosive upon command. So this guy is no joke. He doesn't seem to choke on much either, even on bombs that are larger than both his beak and his head. So we'll forget physics or any sense of reality (was there one here to begin with?) and just assume that Rico can eat any individual item up to the size of an 18-wheeler, although he'd have to take a few minutes to cough it up, and seems to have a practically limitless capacity. He also doesn't seem to be weighed down with anything that he holds, either making him incredibly strong or giving him the ability to mitigate the physical properties of anything he eats. This is weird and not meant to be read into this far, so I won't go much further. Suffice it to say, he routinely coughs up things far larger than himself without batting an eye, and I'll just give Riko the limitations described above, with no adverse side-effects to himself.
In the movies we're seen plenty of stealthy infiltration, and given the penguins' small size it shouldn't be a huge problem to get into the compound quickly and silently. Additionally, Rico could basically store an armored division inside his stomach given what we see in the show, so equipment is not a problem here. We can probably be able to get an enormous amount of grenades of multiple types, at least 2 long guns and a sidearm, and plenty of ammunition to the penguins.
2 days of prep should also be plenty of time to jerry-rig some sort of body armor for the penguins in case they do get in a firefight inside Bin Laden's compound, meaning their survivability drastically goes up. If everything goes even moderately to plan, they should get into close contact with Bin Laden without being noticed. Even if the plan is discovered, we're forgetting King Julian and Mort. They've shown themselves to be fantastic at destroying things in the movies, and armed with whatever it is that Riko can store in his stomach (which, may I remind you, seems to have basically no limit) they should have no problem annihilating anything that tries to escape. Given the penguins' skill at combat, however, combined with the fact that they're tiny, fast-moving targets, they should be basically impossible to take down accurately (certainly not all of them at once), and almost ensures that at least one reaches Bin Laden. At that point, it's almost no contest.
To conclude,the penguins win. Perhaps with limited gear this could be a slightly bigger problem, but equipped and support the way that they are, they should be fine. They win in an outright firefight, which only occurs if they get spotted and don't catch Bin Laden with his pants down. In fact, given how their movies and shows played out, it wouldn't be uncharacteristic for them to wait in the bathroom undetected and quite literally catch Bin Laden with his pants down.
