Is it possible to make pork belly very soft with a pressure cooker?
...a pressure cooker can't really speed up the process for breaking down the fat in the pork belly...


Nope - this isn't really true, nor is it a complete description of what's going on. Pork belly doesn't just contain a large amount of fat, it contains a large amount of connective tissue (which is why it's so tough when not properly slow-cooked). The goal with such cuts (ribs and pork shoulder are other good examples) is largely to break down tough, chewy collagen into gelatin, which provides a deliciously viscous texture. It's sometimes described as "mouth-coating", which sounds... less desirable than it is.

Both the process of melting fat and the process of converting collagen to gelatin are temperature-dependent and will speed up with increased temperature. This is the advantage that your pressure cooker provides. However, the latter process is a lot more complicated; it requires the presence of sufficient water, and it doesn't scale linearly (e.g. it won't get 10% faster by applying 10% more energy). 

There seems to be an upper bound with how quickly you can get collagen to convert to gelatin, and with pork belly there's so much collagen that a typical cooking time might extend into 12+ hours. And that effort is necessary, unless you want a chewy pork belly after all that work. With a pressure cooker, you might be able to get the cooking time down to 9 or 10 hours, but the reduction won't be as drastic as with other foods. 

Additionally, gelatin itself is temperature-sensitive, and pure gelatin will break down if boiled; what seems to happen is that the long, flexible strands that give gelatin its elasticity get "cut" at high enough temperatures, such as the higher temperatures in your pressure cooker, and it loses some of that lip-smacking goodness. I've observed this myself when making stock in a pressure cooker. It's faster and more convenient than letting a pot simmer on the stove all day (and the endless skimming, and topping off with water, etc.) but it never has quite the texture of a stock made the "proper" way. Don't get me wrong: it's still quite good, and pork belly has so much collagen that you might not notice a difference in the end, but there's an argument to be made for accepting the additional couple of hours for a traditional slow braise.

So, the TL;DR: a pressure cooker will indeed speed up the cooking of pork belly, but not as much as it speeds up other cooking.