My answer is from a British perspective.
No, it would not be correct to use piss poor in this context.
Poor in this phrase does not refer to the wealth definition of poor, but to the quality or standard definition. In other words, piss poor means of a very low standard, or low quality. In the UK, it is most-commonly used to describe the performance or effort of a person, group or organisation. For example, if you showed up to an event and it was organised very, very badly, you could describe it as piss poor. Indeed, the alliteration piss poor performance is not uncommon.
Mirriam-Webster corroborates my understanding (this is the only definition given):
Piss-poor: very bad : extremely poor
According to wikipedia, piss poor performance is a constituent of a whole series of slang alliterative military acronyms. For example:
Proper Planning and Preparation Prevents Piss Poor Performance
Those acronyms highlight the idiom's usage in referring to the performance of individuals or organisations (rather than objects, for instance).
Having said all that, I must acknowledge that the Cambridge English Dictionary does define piss poor with regards to wealth:
having very little money: we were piss-poor
But, I have never heard the phrase used in this way in the UK (and I have heard it a lot). Accordingly, the Oxford English Dictionary does not define it like so, and offers the same single definition as Mirriam-Webster. I take that as proof of my contention that piss poor is seldom used to refer to wealth.