No, not really. A blockchain without a native currency is imparted no special economic security i.e. insurmountable costs to rewrite data.
If you want a system that allows anyone to participate and secure high stakes transactions, you cannot allow cheap revisionism or censorship which is exactly what traditional systems allow (through power or bribes). A blockchain without a native currency is void of any economic security.
I'm not sure what you believe the "gotcha" is when your hypothetical removes the most crucial aspect in order to try and prove the tech is useless.