A recent study1 looked at this exact question. Participants used smart phones to scan food barcodes for 4 weeks. The nutrition labels were then displayed for all the products they scanned.
They found that the products for which participants viewed the label, and subsequently purchased were about 13% healthier than the products where the labels were viewed, but were not purchased.
The authors conclude that, "nutrition labels may influence healthier food purchases by those consumers who choose to use them."
- Mhurchu, C. N., Eyles, H., Jiang, Y., & Blakely, T. (2018). Do nutrition labels influence healthier food choices? Analysis of label viewing behaviour and subsequent food purchases in a labelling intervention trial. Appetite, 121, 360-365.