Yes, indeed; the default seed is the system clock (seconds since Jan 1st 1970). Because of the properties of good random number generators (e.g. the Mersenne twister used by HyPhy), the closeness of two seeds imparts no undue similarity to the pseudorandom number sequences genereates from the two seeds and the period of the sequence is enormous (>2^10000), hence there should be no need to select the initial seed carefully.

Cheers,
Sergei