It's an interesting idea. I was ready to shoot it down but remembered an experiment we did at school where we put a white flower into a glass with some food dye in it. Hey presto... food dye appears in the petals of the flower. The same could be true for the flowers of cannabis. Although, you'd be safer just feeding them with some strong solution a few days before harvest. If you jab a syringe into the stem, first of all, you won't be able to inject much into it because the tissue is so dense, it's not like fat or muscle that will move out of the way. You're also going to wreck a large number of the xylem tubes that carry the water up the plant by exposing them to the atmosphere.
You can imagine the inside of the plant as begin lots of tall drainpipes stood in a swimming pool of water. They literally suck up water when a pump up at the top comes on (for plants, the pump is evaporation at the leaves, transpiration). If you drill a hole in the drainpipes down near the swimming pool, they're going to suck in a huge amount of air through the holes and not lift the really heavy water up. If you drill into the cluster of them with a 3" hole saw, which is what your syringe blade would be to the pipes in the plant, you'll cut right through them.
So yeah, I'd go with putting it in the water.
But really, I think you'd be saving yourself time and money and increasing the strength of the flavor if you just water cured the buds in solution containing it, or sprayed it on and air dried.
Be WELL aware that some flavorings may contain sugars and other sweeteners that bacteria and mold will love to eat; potentially wrecking your green.
Personally, even when I smoke blunts rolled from those flavored leaves I can't really taste what it's meant to be all that well. The green is usually the strongest taste by far. I've used flavored rolling papers before. They weren't great, they just made it taste artificially sweet on my lips, nothing special.
