Hi Doug-
Yes, WECo definitely had woodshop departments as did Kellogg and Stromberg Carlson and most of the rest of the manufacturers.
After all they manufactured switchboards, telephone booths, etc. The woodwork was first-rate and often gorgeous.
Even in later years if for example, a addition to an 40-50 year old switchboard was being built, the woodshop would dig out the drawings and patterns used for that customer’s original board and create a perfectly fitting, cosmetically matched, add-on section; without an onsite visit by their carpenters beforehand.