Yes. That’s the idea - in combination with the idea that requests to the same server are often repetitive (they might have a lot of common headers). And „synchronized dictionary“ is basically the idea behind.

Unfortunately http/2 didn’t really give implementations a chance to opt out of that complexity by setting the table size to 0 - the default is 4kB and manipulating it triggers a race condition which might fail requests. That part is thankfully nicer in http/3, and both peer äs have to opt into using dynamic compression via a synchronized header table to support it.