Hi Sam,
The REST adapter which is available in current version(7.3 SP16 / 7.4SP11) is not capable to fetch the exact error message from server, I have checked with SAP regarding this and they were saying that feature is available in 7.3 SP17 or 7.4 SP12 which is releasing in coming November. Also along with this feature there is one more as get the Http header details from receiver server.
Also checked possibility from them , but unfortunately there is no such.