I wouldn't string it.
The Archers Company was in business in the 1920s and 1930s and many of their bows are highly collectible. If shooting an 80 or 90 year old bow, it probably isn't going to hold up long before it breaks.
Desirability would depend on condition, wood type, backing type, water transfer decal style, branding into wood, horn nock style, grip style and material as well as the city and state it was made if on the decal. Most were from Pinehurst North Carolina, but they were located in three other cities over the years.
Give us some more details about the bow.