That is hard to answer, It depends on exactly which bit is corrupt, Think about it like this, maybe like 99.9% of your dump is not very important, what I mean by that is you can replace it with dump from another console and it will be fine, but you need to get that 0.1% (Console specific info) from your own console perfectly or it will never boot again, so if your complete dump is randomly corrupted in some places, maybe you could be lucky and still get your console specific info from it, hard to know until you dump it.
I would guess that as you only installed a PUP rather than messed up with a flasher, and that PUP completed installation, then there is a
good chance your console specific information is still ok, but of course its not 100%..