Generally, yes, it's possible. Often not too complicated, either.
Generally, your internal network is logically one network topology (i.e. you can route from anywhere to anywhere, again, internally).
Also generally, there's some "one router" which has the "connection" (or next hop path) for Internet traffic. If non-interior traffic (e.g. Internet bound) gets to this router, it goes to/from Internet too. The tricky part is how "all" your Internet traffic "knows" to use this "one router".
Sometimes if your main site is small, there's only one "one router" and so other routers, like those at remote sites, don't know to send non-interior traffic to it.
So, for any router that needs to "know" to send to the "one router", generally, either you use a default static route, on all such routers to direct non-local traffic to the "one router" or, if using a routing protocol, you dynamically advertise a default router via your routing protocol.
Once traffic gets to the "one router", again, generally, it doesn't make a difference where that traffic came from within your interior network. Things like NAT and interior routing should work like they do for just your DC site.
