Well, can it, when it is in direct contact with the components and circuitry?
Ignoring the specific issues with aluminum there are production issues with the concept in general. If the components and PCB are covered with a non-conductive layer then how do you make electrical connections between them?
You need to first remove the insulating layer. Doing this mechanically would be tricky and risk damage to small parts. Doing it chemically would avoid mechanical problems but you need to find some chemical mixture which will dissolve the insulating layer but not the underlying conducting material, won't damage the parts and can easily be remove at the end of the process. Any problems with any point in this process would result in high resistances or mechanically weak joins.
To a certain extent the problem with having to remove a thin layer already exists in conventional manufacturing, there is a layer of dirt and oxidized material on all of the parts already. It may be conductive but it causes reliability problems with the joints. That is why you use flux when soldering, to chemically remove the dirt when making the joint.
For fairly clean things you can use a mild flux that will be inert fairly quickly (a no-clean flux), for dirtier items you need a more aggressive flux. If you fail to then clean any remaining flux off the board (which involves some nasty chemicals) this flux can eat away the joints over time.
There is also the metallurgy issue. The solder needs to melt at a low enough temperature that a brief exposure won't damage the components. The solder will then form an alloy with the metal on the PCB and the parts, the crystal structure of that alloy has to be compatible with the structure of the underlying metal or the joint will be weaker.
This is why 63/37 tin/lead solder was so good, the underlying metallurgy was as close to perfect as you could get. The current silver/copper/tin solders aren't too bad but they aren't as good. As soon as you add gold plating you start weakening the joints, the gold alloys that form are mechanically very poor.
Or the short answer: A method of making electrical connections that is reliable and suitable for mass production is a lot more complex than simply picking a metal to use. Rather than compromise the electrical characteristics for something that's waterproof it's far simpler to use a normal process and then add a layer of conformal coating if needed.
That looks like a hydrophobic membrane. These have low surface energies and the force of attraction to the water is less than the surface tension of the water. Because of this the water is able to "ball-up".
Figure 1. Surface energy measurement. Source: Rame-Hart.
Surface energy is a problem in printing on plastic substrates, for example, as water-based inks won't wet. Solutions to the problem include corona treatment to increase the surface energy by knocking out some hydrogen atoms from the polymers and replacing them with oxygen atoms. This, in simple terms, provides more molecular hooks for the water.
The strength of attraction between a material and a coating is determined by the relative surface energy/surface tension of the materials. The higher the solid’s surface energy relative to the liquid’s surface tension, the greater the molecular attraction, this draws the paint, ink or adhesive closer for high bond strength. The lower the solid’s surface energy relative to the liquid’s surface tension the weaker the attractive forces are and this will repel the coating. Source: Dyne Testing.
I would be afraid that thermal cycling will expel air from the enclosure and then, on contraction, suck water through the membrane. I would look for a sensor that could be mounted through the outside of the enclosure or read through a tube terminated on the casing.
Figure 2. A pnuematic bulkhead fitting.
Figure 3. A bellows diaphragm. Source: AP Racing
On further thought, if your pressure variation is modest a bellows diaphragm would allow the pressure to equalise while maintaining weatherproofing. Put the bellows on the inside. The photo is some sort of car part but it might get you started on a search.