I apologize for using the term "sea shell"; I'll use either "snail-shell style" or "trumpet style" in the future - in an attempt to clearly distinguish the two styles of horn bodies that GM used on old "Stovebolt era" trucks (at least from 47-52).
In older (pre-1947) parts manuals, GM used the term "projector" for the output piece and the term "backshell" for the part/parts behind the "projector" on both styles of horns.
The GM illustrations that I have only show the two (snail-shell) horns in 1947-1952 sales/data-book illustrations.
No relay is displayed (or stated/referred-to); however, a horn relay was available for horns from 1934 onwards.
Before 1947, a long straight-neck "trumpet-style" horn was available as optional equipment. It is not clear what style, if any, standard-equipment horn came with these older trucks.
Maybe Brad or another member has installation instructions for the pre-1953 (47-52) GM accessory dual "snail-shell style horns"?
The installation instructions would show the relay, if it was provided/used prior to 1953 (my guess is that a relay was provided with those dual horns?).
Back to Ed's original post/question: a relay was not used as standard equipment with a single horn in 1951; however, a relay was available as an accessory. It will not hurt (and, it might help).