It is absolutely possible,one simply needs a host device to control read and write the information to their respective drives.However this would require a vast knowledge of electronics and programming.
A year or two ago we worked out a way that one could do it by using a tiny (and I mean TINY) linux computer (yes....a computer...but REALLY TINY!!) to host the devices,however,the project was scrapped as it would cost hundreds of dollars to build the unit as well as hundreds of hours spent programming it,designing the circuits,and also there would be zero chance of it fitting inside the psp.It's just generally a bad idea,wait a year or two,sandisk and sony will be coming out with 1tb upwards portable storage and you can play ps1 to your hearts content!