To answer your question, yes it is possible to make this work. There are several ways that you can go about it.
Routing - If the router has some OSPF relationship with the next hop routers in areas 1 and 2, then it can be informed of loss of connectivity to networks that are further downstream. The router will then revert to the secondary connection in order to reach those networks. This will work especially if routers in Area 1 and Area 2 pass on default network information, meaning that the router will be informed of the default network. You can adjust interface costs in order to influence the OSPF routing so that the MPLS connection is preferred.
IP SLA - Using an SLA such as a ping to a particular network via the first interface, in the event that a ping fails, you can insert another alternate route into the routing table. More about this can be found here:
I’m not clear from your diagram if the interfaces connecting to the slow and fast connection are actually found in areas 2 and 5. Because you label them as Area 2 and Area 5 I assume the interfaces are participating in OSPF in those areas. If this is the case then yes what you propose will work. However, keep in mind that it will not load balance, if that was what you were looking for. By changing the cost, you are causing one link to be preferred over the other. If the link fails, then OSPF will reconverge and the other link will be preferred. OSPF does not support unequal cost load balancing.