Is it possible to configure Oracle's CONNECT THROUGH based on roles?
A.B.Cade and Phil gave the answer in the comments:

CONNECT THROUGH cannot be granted using a role.  

As Phil said, creating a script to do this is trivial.  Be aware the database links do not work the same when used via proxy.

This situation does have risk, but given the requirements and limitations in Oracle, it is sometimes necessary.  You might consider allowing the script to accept two usernames.  The DBA can then run the script on demand for the particular client and support person combination that needs it.  By revoking the privilege when the support session is complete there will be less the potential for abuse.