Is what you want technically possible? Probably.
In an earlier era, you could have a network or an image scanner or other devices connected to a host via SCSI; via a storage bus. There was all manner of odd SCSI-connected gear. (Think of SCSI as expensive multi-host USB with big expensive cables and with expensive peripheral devices, and you'll have the general idea. And FWIW, SCSI is the underpinnings of USB.)
You would end up writing a whole lot of driver code for the devices and hosts you have, too.
Which is where folks end up with commercial SAN solutions, or with NAS solutions, and not with using a SAN as a network.
The various Fibre Channel controller vendors discussed but never seemed to have sorted out the network interface designs for their FC controllers.
If you want to roll your own storage arrays akin to the [Apple Xsan|http://www.apple.com/xsan> or the HP [MSA|http://h18000.www1.hp.com/storage/disk
storage/msa_diskarrays/sanarrays/index.html] or [EVA|http://h18000.www1.hp.com/storage/disk
storage/eva_diskarrays/evaarrays/index.html] SAN arrays, well, have at. You'll likely end up needing to write host disk drivers, as well as the firmware within the SAN controller. Networking drivers might be a bit more tricky; I haven't looked at those device interfaces in a while, and you'd need to tie those drivers into the host network stacks. Once you have some or all of that working, then the hosts can see the block storage out on the SAN. If you need sharing, you'll need to sort out a cluster or SAN file system to run atop the block storage or atop the network connection you've built; a file system that can coordinate distributed access.
Possible? Sure. On a budget? Probably not.