Not familiar with that processor, @markjw if pretty good with judging proc spec.
Looking at other spec if thats stock should suffice, if its a single terminal you could just use localDB rather than SQL.
Failing that a SFF desktop in the office or something as a sql server and network them up.
My stock setup is a Core2Duo USFF Dell which isnt the latest and greatest.
If you find it sluggish you could disable some of the unnecessary windows features.
Would also depend on how custom you intend to make the automation, a basic setup obviously would be less demanding than a highly customized setup with loads of scripts and complex constraints.
I think it should be fine. Agree with JTRTech that you should just use LocalDB if only single terminal, it will mean less resources used on the system.
Up until just recently (when we moved to J1900 systems), most systems we sold were running Celeron 1037U processors with 2Gb RAM, and worked perfectly fine both as single terminal and terminal + SQL Server for multi terminal setups.