No, doubly efficient IPs do not have much to do with ZCash. deIPs are currently too weak to prove the general NP statements that ZCash requires.
ZCash relies on a different kind of "proof" system: SNARKs.
There's many differences between the two:
a) deIPs assume a computationally unbounded adversary, whereas SNARKs assume a polytime adversary.
b) deIP constructions currently suffice only for a limited class of languages, whereas SNARKs can prove any NP statement.
c) SNARKs have zero knowledge variants, whereas it is not clear how to extend many deIP constructions to be zero knowledge without changing the model (ala https://eprint.iacr.org/2017/305).
d) Most deIPs are interactive proof systems, whereas SNARKs are non-interactive.
ZCash relies on a different kind of "proof" system: SNARKs.
There's many differences between the two:
a) deIPs assume a computationally unbounded adversary, whereas SNARKs assume a polytime adversary.
b) deIP constructions currently suffice only for a limited class of languages, whereas SNARKs can prove any NP statement.
c) SNARKs have zero knowledge variants, whereas it is not clear how to extend many deIP constructions to be zero knowledge without changing the model (ala https://eprint.iacr.org/2017/305).
d) Most deIPs are interactive proof systems, whereas SNARKs are non-interactive.