Sometimes it matters a lot.
Shepherd’s purse does much better as a fresh plant tincture as does cleavers.
One thing to remember is that fresh plants can contain a lot of water. To be preservative, alcohol must be around 30%. So if you use 40 percent vodka to tincture a plant with a lot of water content you may dilute the vodka enough that it is not preservative. When I tincture fresh Plants I usually use Everclear to prevent this problem.
As to the flower fluff question, if the flower is medicinal it’s fluff is medicinal. Use it.
Doc
Don't use herbs or combine herbs with medications or use them during lactation or pregnancy without talking with your healthcare provider.