I have never seen anyone not configure the gateway on the server. If your server is performing forwarding DNS, (meaning an iterative query on behalf of the clients), I could see performance issues on your domain.
The server will need information from beyond the router. If there is no direction to the router, I can't see how this will not seriously impede performance on the domain.
I would expect intermittent web pages, the inability for some clients to go to web pages from time to time.
Now, that's just DNS. Let's talk about DHCP for a second.
Let's say you create VLANS for your system and use a DHCP relay. That requires L3 IP routing. So, if there is no pointer to the gateway, you will not be able to administer DHCP on VLANS that are not on the same subnet as your server.
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With that said:
You will not be able to get an outside time source because it uses IP routing at the L3 level. Since your DC does not have a gateway set, time will not be able to synch from an outside time source.
Your DC, by default, should be braodcasting its time to all clients on the domain. These clients will synch up, as long as they are not within a +/- 5 minute phase offset. That means if they go beyond +/- five minutes, they will synch up to the server. You can adjust the phase offset in registry.
Bottom line::::
1) without a default gateway, your going to have problems with anything that uses L3 routing and requires server assistance, (like DHCP relay, replications between sites, DNS (if using forwarders), ect...)
2) You will not be able to synch with an outside time source.
3) your clients will synch up if they are out of the 5 minute threshhold