Its not quite that simple, because each routing protocol can have additional conditions that must be met.
EIGRP certainly does and that condition being that neighbours MUST be addressed from the same subnet which you will not be true in your particular circumstance.
OSPF will require testing. OSPF may form an adjacency and allow LSA exchange. The real test is whether it will insert the learned LSA's into the main routing table given that the neighbours are on two different subnets. If it does you are homefree. You can then tune the hello timers as required.
As your stated objective is to make your connectivity more robust, keep the setup as simple.
And as Vince indicate what out for the MTU hit with GRE tunnels.
Also for GRE tunnels remebber to configure a static route for the tunnel destination address to prevent recursive lookups.