Well only the adults can climb, the nymphs lack any climbing ability whatsoever.According to roachcrossing, Parcoblatta fulvescens is a good (prolific) feeder, though they can climb and males can fly. Also, they're much smaller than S. lateralis (18mm vs 30mm), so that may be good or bad depending on your needs. The climbing may prove to be a headache in feeding your tarantulas, unless they are arboreal.
None of the Parcoblatta species burrow, but they may take advantage of large particles of loose substrate and hide under them when disturbed.Thanks for the answers. I was reading on Roach Crossing that P. fulvescens don't burrow. Do other Parcoblatta burrow like P divisa and P. lata?