Yes, this is possible but they will have to create it. Start with the Exalogic Guest Base Template (EGBT), available from eDelivery, which will have the base linux (e.g. OEL 6). Then install all the software desired, make configuration, etc. Once they have the vServer the way they want it, create a template from the vServer using one of the following methods: instructions in the documentation (http://docs.oracle.com/cd/E18476_01/doc.220/e25258/appendix.htm#ELCLD77142), the script made available from MOS Note "Script: To Create a Template from an Existing Guest vServer (Doc ID 1596209.1)" or using the Exalogic EKIT (see MOS note: "Exalogic Kinetic Infrastructure Tools (EKIT): Set of scripts that provide common reusable command line infrastructure actions for Exalogic virtual platforms (Doc ID 1933252.1)"). I personally prefer the EKIT but this does have to be installed separately first.
Hope that helps.