Not a great idea. As others have suggested its sugar concentration that inhibits biological activity. Having had some exposure to the science of this in the preserves industry you get no fermentation or moulding if the concentration is 67% or over (and STAYS that way) and very little at above 63% solids. Hence 2:1 syrup at 66.6% is very popular in the periods when consumption might be slower (but we only use approx that as it is stable stored in IBCs, have done so for up to a year).
If you get a full analysis of honey, among the minor items reported are yeasts and moulds...the spores etc are just an environmental incidental occurrence.. not that your honey is bad....and could be triggered into growth in the syrup if you add honey to it.
However, for me the biggy is the possibility, even at low levels, of pathogens in the honey. You may not have clinical EFB or AFB...do not wish that on my worst enemies...but if you have sub clinical around, completely unseen and no criticism of beekeeping intended, you might inadvertantly be sowing the seeds of an outbreak in the medium to long term. Oldest rule in the book...do not feed honey..esp if you are unsure of its status.
Appreciate the amount in question is very small and the likelihood of harm is approaching (but not actually) zero.