It is theoretically possible for a poorly designed “pseudo-random algorithm” to be stupid relative to the search space; for example, it might always jump in the same direction. But the “pseudo-random algorithm” has to be really shoddy for that to happen. You’re only likely to get stuck with that problem if you reinvent the wheel instead of using a standard, off-the-shelf solution.
You don’t need that much shoddiness to get very weird things in certain situations (IIRC there was a PRNG getting some value wrong by 20 standard deviations in a Monte Carlo simulation of the Ising model because of a non-zero three-way correlation between the n-th, (n + 63)-th, and (n + 126)-th outputs or something like that), and some off-the-shelf solutions are shoddier than you may think.
You don’t need that much shoddiness to get very weird things in certain situations (IIRC there was a PRNG getting some value wrong by 20 standard deviations in a Monte Carlo simulation of the Ising model because of a non-zero three-way correlation between the n-th, (n + 63)-th, and (n + 126)-th outputs or something like that), and some off-the-shelf solutions are shoddier than you may think.