Yes, it is possible - QLogic (at least) HBAs support IP over F/C, and many switches also support it. However, if you want to push large amounts of data across it you are in contention for bandwidth with the disks, so you may have to keep an eye on total utilisation.
You may need to get extra licensing for your switch to support IP.
F/C is possibly the most expensive networking technology in widespread use, so unless you are really stuck with it, you are probably better off using something else. If you have standalone servers then 10Gbit Ethernet or Infiniband is probably cheaper for the bandwidth than fibre channel.
If you're using blades then you're pretty much stuck with whatever is supported by the blade chassis. If the HBAs in your blades support IP over F/C then you could use it. See if the chassis can be upgraded to support Infiniband.