Yes you can prioritize the traffice going outside the switch to the router so that the QOS will get in place on your 3560 device and apply the policy on the outgoing interface of 3560 which is connecting to router.
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Over MPLS links, eh? Is there many-to-many site traffic? If so, you'll want to work with your provider on a QoS scheme. Normally you mark traffic with different ToS settings, and provider treats traffic by its ToS markings.
If you only have one logical link, you can "shape" on your 3560 for the available WAN bandwidth before you pass the traffic to the managed ISP routers. (If there congestion because of shaping, you also prioritize your traffic as desired.)
If you have hub and spoke, you'll need something better than a 3560.