From what I’ve read here it is ok to mix the 2 and apply it like that when it is still completely dormant. Combined they could burn new leaves.
This is just me reading threads here, like the Low-Impact Spray Schedule (2019 Edition). I’ll defer all questions to someone who actually sprays, as my knowledge in this area is purely based on research.
Also, I’m referring to just sulfur here, not lime-sulfur, which as I understand it is really hard to get nowadays and potentially dangerous to make yourself.