Can you tell what routing protocol was used to discover route by examining the adminsitrative distance on said route?
Yes, if you're careful.
On Cisco routers, the routing table shows the administrative distance (AD) of each route. Since AD is an attribute of routing protocols, it can tell you which protocol was used to learn the route.
However, AD is configurable, so you can't assume the default values are being used. You can check what the configured AD values are with the command
show ip protocols.
When multiple routing protocols are configured in router. And when for specific destination multiple routes are available with different routing protocols . Router chooses Administration distance as attribute to choose route among available routes AD with lowest values will have high priority..
Default AD values are
Directly connected--0 Static routing -----1 EIGRP routing ------90 OSPF routing -------110 BGP External -------20
We have feasiblity to change value as per our design and requirements.