If a product contains probiotics, that is contains healthy or good bacteria, then yes heat will kill the microbes. To be on the safe side, let the syrup cool to room temp then add whatever.
Looks to me, honey b healthy is a feed supplement, no microbes, contains essential oils and feed stimulates(?). I do not know for sure what the ?stimulate? is. If the stimulant contains enzymes, understand heat destroys most enzymes.
Blessings