The opposite actually. Its been proven some drafts resulted in many more republicans being called up for service and there are sinister theories why this happened.
The democrats at that time were reactionary populists AFAIK and “the left” would probably have been smaller socdem, demsoc and communist parties, as well as labour unions.
Similarly, Republicans have always been the party generally considered more closely aligned with business, in the sense of leaning toward laissez-faire capitalism, etc. In this respect they inherited the platform from the Whigs, such that this particular alignment of the two major, dominant parties goes back to the Founding of the United States.
[1] See page 3153 at https://www.govinfo.gov/content/pkg/GPO-CRECB-1890-pt4-v21/p...