Yes, you can add sugar, honey, or syrup to a vinaigrette without breaking the emulsion. In fact, they can help stabilize it and enhance the flavor.
A vinaigrette is an emulsion of oil and vinegar, which naturally want to separate. Adding an emulsifier like mustard helps to keep them together. Sugar, honey, or syrup, being viscous and slightly sticky, can also contribute to the stability of the emulsion. They increase the density of the aqueous phase (vinegar) and help to suspend the oil droplets more effectively. Furthermore, the sweetness balances the acidity of the vinegar, creating a more palatable and complex flavor profile. When making your vinaigrette, add the sweetener gradually, whisking continuously, to ensure it incorporates evenly and doesn't weigh down the mixture too much. Start with a small amount and adjust to your taste preference. The key is to whisk vigorously or use a blender to create a stable emulsion.
If your vinaigrette separates quickly despite adding a sweetener, try adding a small amount of Dijon mustard. Dijon mustard contains lecithin, a powerful emulsifier that will help bind the oil and vinegar together for a longer period.