Well there are formal studies of honey on milk kefir growth, wich shares a lot of the same bacteria. The paper
PAUCEAN, A., MUDURA, E., JIMBOREAN, M. A., & MAN, S. (2011). The influence of honey addition on microbiological, physicochemical and sensory characteristics of a kefir-type product during shelf-life. Bulletin of University of Agricultural Sciences and Veterinary Medicine Cluj-Napoca. Agriculture, 68(2).
http://citeseerx.ist.psu.edu/viewdoc/do ... 1&type=pdfIn any of the studied levels 1%, 2.5%, 4%, the honey addition increased the microbial density of lactococi at all the sampling intervals and probiotic bacteria were present at a high level during the product shelf-life. Honey had no effect on pH and lactic acid levels of the final products. Honey at 2.5% and 4% significantly decreased the syneresis (p<0.01) and increase the kefir’s consistency. The sensory evaluation indicates that 2.5% honey added is the optimum level for the kefir-type product.
And the paper
Fiorda, F. A., de Melo Pereira, G. V., Thomaz-Soccol, V., Rakshit, S. K., & Soccol, C. R. (2016). Evaluation of a potentially probiotic non-dairy beverage developed with honey and kefir grains: Fermentation kinetics and storage study. Food Science and Technology International, 22(8), 732-742.
Found it did not impact production and conclude
"After 35 days of storage, honey kefir beverage maintained
its chemical characteristics and microbial viability as required to be classified as a probiotic product."