If you have your router correctly configured and your HT-502 is correctly configured - it shouldn't be an issue having it behind the router. If you are BYOD and haven't set up a STUN server, I would suggest it if you decide to keep in behind the router. I think the provisioned 502's are set up with a STUN server (maybe someone could confirm this). You should not have an issue accessing your home network passed the HT-502, but without knowing your network setup I can't say whether some tweaks to your HT-502 or network may be required. I guess try it is the best way to see. I don't have a problem getting past my HT-502, but I am running a network server and there is no issue logging on to my domain, but most home networks are not setup this way.
If you have registration problems, you will probably need to hard code a DNS into your 502 (again BYOD not provisioned) as mentioned in this thread. I am using DHCP but the DNS it accesses is pretty fast hence a non issue. If you are setup as DHCP you are most likely accessing your ISP's DNS and may or may not be lagging. Hope this helps and doesn't muddy the waters worse.
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