Here's the scenario: An enterprise network with an MPLS core and two branch locations connected to their own Provider Edge (PE) router. In addition to the MPLS link, the PEs are also connected via a DMVPN tunnel. The PEs are peering via iBGP (of course) and are also OSPF neighbors on the DMVPN. Both Customer Edge (CE) routers at the branch are OSPF neighbors with their local PE.

Task: Use the high speed MPLS network as the primary path between the CE routers and only use the DMVPN network if the MPLS network becomes unavailable.

Question: Is the solution as simple as adjusting the Admin Distance (AD) so that the iBGP routes are more preferred?

In Cisco IOS packets are forwarded through the router (or Layer 3 switch) by Cisco Express Forwarding (CEF). A data structure called the CEF table contains a list of known IP prefixes and the outgoing interface that packets should be put on in order to get them onwards to their destination. That's well and good. But how do the IP prefixes make it into the CEF table? To answer that question you have to work backwards and understand the order of operations that IOS goes through in order for a prefix to make it into the CEF table.