Hi Carole ,
BOE 3.1 SP5 is supported with Office 2010 Max.
So, Answer is NO.
I would also request you to check 2 links below :
For PAM (Supported Components 3.1 SP5 ) : http://scn.sap.com/docs/DOC-20551
For Support on BOE 3.1 ( Since the Mainstream support is ended for it ) Very important :
Hope this will help.
regards,
Mahak