No, a switch wouldn't be able to help you since the data that you're working with is higher in the OSI reference model than a switch can handle. Switches are only able to think about packet transfers between hosts attached to that switch. A switch's most common question is, "Is this packet destined for a host connected to me?" If the answer is "no" then the switch will push it to the "Outbound" or "Uplink" port and be done with it. Switches only understand MAC addresses.
A router on the other hand can work with IP addresses. With IP addresses you can get routing tables which provide information about how to get from one IP address to another. If you were to plug in all three ISPs to one router (and the router could handle that sort of thing) then the router would see three possible paths for data to flow over. It would then use some routing algorithms to decide which path to send data over.
What would the purpose of this setup be? Load-balancing? Failover? When would you select one connection, and when another? – Ansgar Wiechers – 2012-09-04T12:48:58.877