I have a client who is currently running server 2003 Std and they want to integrate Exchange Server into their domain. They also have SBS 2003 R2 sitting there on a spare server that is not being used. Now is it possible to use the SBS server for the sole purpose of Exchange in the current domain? Or is there a better solution?

No. SBS has to be the first domain controller in an organization. Because of this intentional restriction you would not be able to use the software in this manner.