Can I power the 45 Series blocks from my pedal power supply board?

Basically, no. The +24V Microblock PS-24 power supply is completely incompatible with the -9V pedal standard. The center pin is made to be different to further discourage mis-connecting. 

However, it should be fine to plug the PS-24 power converter into the AC accessory outlet provided on some pedal supplies. 

It should be noted however that you can power the SuperBlock series from your 9 volt source.