Yes they do but BEWARE that the price listed isn't what you're going to pay. I bought my Spy bag from them and ended up paying $90 more than the listed price.
Yes Styledrops sells authentic bags. I bought a Hogan bag for $900 there. The only catch is when you use a credit card to pay - the credit card company will most likely they will charge you the international transaction fees - 2-5% of the total amount. I found this out the hard way when I got my credit card statement.
There's a Marc Jacobs box bag on there that they were trying to sell for just over $1400, but that bag was originaly only $995 in the store and I just picked it up on sale at Barneys for $399. What's up with that?