Can Pseudorandom values be used as secure keys?
Yes and yes, as mentioned in the comments.

It is worth noting that Bitcoin wallets use a scheme similar to this in BIP32, a method of creating n various EC keypairs from a single seed deterministically:

https://github.com/bitcoin/bips/blob/master/bip-0032.mediawiki

EDIT: This answer only holds true if  is a CSPRNG.  (This application is sort of why the definition for CSPRNG exists.)