Nope. If a Southern Leaguer has a Piedmont back then it will be 350 Series. Southern Leaguers were printed in "Group 6" as described here:
https://t206resource.com/Print%20Group%206.html
The first printing and distribution of the southern league group was with Hindu brand cigarettes beginning in August 1909. Though advertisements indicate that all 48 subjects were to be produced at this time, only 34 were printed due to a short production run and printing limitations. Per the Hindu advertisements, these southern league subjects were packaged and distributed separately from the major-league subjects of the 150 Series.
After the Hindu campaign, the 150 Series concluded and the 350 Series began.
During the first printings of the 350 Series, the complete southern league group of 48 subjects were printed with Old Mill and Piedmont brand backs. The Old Mill (Southern Leagues) back advertisement was designed and printed specifically for use with this group and was applied only to sheets with these subjects. This is evidence that the 48 southern league subjects were printed on sheets composed of only southern league subjects. These preprinted front sheets had either the Old Mill (SL) or Piedmont 350 backs applied. After these early 350 Series printings, the southern league print group was discontinued.