@DavidNofre:

"If I am allowed to speculate, I wonder if we shouldn't look at the developments of the early 19th-century, and specially the interest on mechanical agency and language, as Mark has put in, rather as part of the longer tradition of automata construction, and particularly late 18th- century fascination with speaking automata (see, most recently: Kang's Sublime Dreams of Living Machines and Adelheid Voskuhl's Androids in the Enlightenment)."

Yes. This also brings in a discussion of analog computing which is reflected by these mechanical automata
(e.g., principles of program, memory, iteration, and conditional branching in the form of a geometric discontinuity 
are intrinsic to these machines): http://dl.acm.org/citation.cfm?id=2601391 . As to when 20th century computing
theoreticians used the word “automata,” I wish I knew.

-p

Paul Fishwick, PhD
Chair, ACM SIGSIM
Distinguished University Chair of Arts & Technology 
   and Professor of Computer Science
Director, Creative Automata Laboratory
The University of Texas at Dallas
Arts & Technology
800 West Campbell Road, AT10
Richardson, TX 75080-3021
Home: utdallas.edu/atec/fishwick
Blog: creative-automata.com