I get why this question pops up so often — the PSP Go is a weird little cousin in the PSP family. From my tinkering and buying habits, here’s the clearest way to think about 'Dead Head Fred' and a PSP Go: the Go cannot read UMD discs, so any UMD-only release won’t work natively. The PSP Go relies on digitally purchased games through the
PlayStation Store (or content you’ve legally transferred to the device), so if 'Dead Head Fred' was sold as a downloadable PSP title on the store, you can play it on a Go. If it was only released as a UMD and never appeared on the PS Store for download, then the Go won’t run it without unsupported hacks.
A few practical bits from my experience: licenses live on your PSN account and can be region-locked, so you’ll need to buy the game from the same region/store tied to your PSP Go. Back in the day I used Media Go and a PS3 to manage purchases and transfers — that workflow still matters if you have older purchases. Also, PlayStation sometimes delists older PSP titles, so a game available a few years ago might not be purchaseable today.
If you’re unsure whether 'Dead Head Fred' is in the store, check the PlayStation Store on your PC or on a PS3/Vita logged into the same account. If it’s there, you’re set; if not, your options are finding a digital re-release or accepting that the Go won’t run the UMD version. Personally, I’d search the store and community threads first — saves buying blind and feels better than chasing rare UMD copies that can’t be used on the Go.