The router will use its local static route over the route learned from the opposite router first due to the distance metrics of static routes over OSPF routes.
If the link connecting to the gateway as specified in the static route is unavailable then this route will be removed from the routing table and the route to the same destination (via your 2nd router) will be used (as learned by OSPF)
I have done similar using dual MSFC's in 2 x 6500 switches both running OSPF, each 6500 switch was connected to 2 other switches (for resillince) If one of the remote switches was down/or link failed then using OSPF traffic would be routed via the switch that was up.
HTH
Paddy