The short answer is "no".
The long answer: HA across different geographical sites brings a few caveats that a simple 340 box just can't handle. I believe 440 and above will provide the GSLB functionality you need to do this right (and even then, local HA is still a good idea). The first issue is the distance and associated latency between the two locations. Failover in this environment may take longer than you want, and depending on what the backend requirements are (do clients need to initiate connections outbound from site 1, through the 340 at site 2, is connection mirroring functionality available so connections can continue seamlessly on failover, etc), so it's difficult to do anything other than a standard DR failover from one site to the other. The other issue is the inbound connections. The GSLB is what changes the client resolved address to the virtual address of the box at site 2. This would be problematic and slow if the external connection to the internet is what fails (in an active/active GSLB environment, this still happens, but is less noticeable to the end users). Having a back channel such as an MPLS link between the devices and using the LAN side of the 340 for availability checks helps here, but that is not always available, and I'm guessing with a 340 you're not dealing with an expensive MPLS link have an IP block big enough to share IPs across two sites. Admittedly, I could be generalizing there, but if that's not the case, you may be able to take advantage of some of the aforementioned options noted above.
Finally, there is the fact that the 340 is under-powered from a feature/function standpoint to do all this (failover on internal interfaces, GSLB/DNS load balancing, re-rerouting traffic across MPLS on failure, etc.) to do this. A bigger box or the VM might be a solution, but ultimately you have to re-architect the solution and consider another device for the DR site instead of splitting a local HA pair into two and trying to do GSLB with them.
Hope this helps.