That is pure security by obscurity. If I know the output of the PRNG, and that this method is being used, I also know the random number. So attacking it is no harder than attacking the PRNG itself.
Wouldn't the weak point in that system then be the PRNG? If so, doesn't that require the use of a crytographically secure PRNG in the first place?
I'm not ready to disagree with you (yet) but I was thinking about the possibility of turning a pseudo-random number into a truly random number. If you generate a number using a PRNG and use that as a bit offset (via the timestamp), you might get a better string of random bits as an input to your cryptography system. Of course this relies on there being enough previously generated bits available.