Welcome to the board, I've never heard of Emerald Dolphin so I can't give a arefview on them.
The current can varry so there is no real short answer to the drift diving question, although most of the time the current is very gentle and the drift is just enough where once you get more experianced as a diver you will be able to get neutral boyancy and just "hang" in the water and let the current move you along at a leasurly pace without having to kick at all. no, you won't be moving so fast that you will miss the sea life, and if the current is wanting to push you past something you want to observe longer, usually you can just turn your head into the current and kick gently against it and hover over what you want to see.
the only time I have ever had a really bad current is on my most recent trip we made a night dive and the current was incredable! we we're literally flying thru the water, it felt like being in a car going about 20-25 mph. but this is when hurricane Francis was passing by Cuba and i'm sure that was causing the unusal conditions because the next day it was back to it's regular gentle self.
In other words, just sit back an enjoy the ride, you'll love it the way the rest of do.
welcome to the undersea world, give us a trip report when you get back,
best wishes and happy diving.