Yep there should be no problem using your USB HDD with the memor32 thingy and HD Advance.
Things to note. (Other members correct me if I am wrong)
USB HDD has to be formatted FAT32.
You will find the loading of games slow as the USB in the PS2 is only v1.0
You will find the streaming of movies within games might breakup or be slow because of the USB v1.0
Some games don't work with the HD Advance, but there are not many
You can use a hdd to boot games form it but you need usb extreme to use a usb hdd. hd advance is only compatible with a hdd connected with a network adapter and only with the fat ps2's.
I'm not sure if memor32 has a new firmware enabling games booted from usb hdd, there was one in the pipeline.