You can get to the caps but it will be messy. The filter box is probably potted with tar, pitch, or wax that will have to be melted out in a warm oven after the rivets or screws holding on the cover are removed.
If you are lucky, the filter box has all of its internal components brought outside the box with separate wires that are then soldered together as needed on terminal strips under the chassis. This makes it possible to disconnect a bad internal capacitor and wire in a new one under the chassis without having to dissect the old filter box. If the box is designed with "buried nodes" then you will be stuck with having to dismantle the box.
A bad choke is more problematic but if your set works at all, the filter chokes are probably OK.
Not sure why radio manufacturers built these sets this way in the '20's. It certainly complicated servicing them; although the capacitors seemed to be remarkably long-lived. I have a Bosch Model 28 that has the original filter box and which still works fine, 84 years on. Fortunately, it is one of the sets that has all of the components in the filter box brought out with separate leads, so bypassing is a possiblity if (when?) one of the internal caps or chokes finally decides to "let go".