Yes it's feasable, but why are you NAT'ing so many times*? Is there a problem with your network numbering? Supporting legacy addresses where people haven't configured things correctly?
One thing I would note is that I'd normally configure the F5 directly in front of the servers. (Usually by moving the serves to a DMZ behind the F5's). The internal firewall doesn't seem to be gaining you anything... (** Assuming this is a new requirement and not simply a new requirement to load balance existing internal only servers from external).
e.g.
Internet -> Firewall -> (F5 -> Servers) all in a DMZ.
or
Internet -> Ext Firewall
\
F5 -> DMZ with Servers
/
Internal -> Internal Firewall
(So the F5 becomes the router to/from your DMZ's).
More info as to your reasoning & what can or can't be altered may help...
H
* - I don't adhere to the commonly mis-stated view that NAT'ing is automatic security...