Depends on the connectivity between core switches and routers.
If each router is connected to each core switch with L3 links and each router receives routes from the WAN with the same metrics then yes the core switches would use both routers.
And yes you could influence the path a number of ways ie. you could increase delay bearing in mind you would do it on the router interface connecting to the WAN or the core switch interface connecting to the router.
Or you could use offset lists either on the routers or the core switches.
If the connectivity between core switches and routers is not as I described please clarify.
Jon