Correct. Nothing mutually exclusive about it, really. It was actually a fairly common arrangement in past decades, and is still used today on some boats. Many builders beyond I.P. have used it, Hinckley, Bristol, Allied, to name a few.
I have such arrangement on my boat, I love all aspects of it, except centerboard trunk. I can live with a trunk, it makes a table.
Very shallow draft. Low wetted surface for downwind sailing. Good upwind performance. Good tracking.
If you bump a bottom, - just raise the board and you are free.
I can beach the boat for maintenance. Hull is shallow enough that razing water floats it without flooding.
IMHO, it is ideal combination for shallow waters, read, all east coast and Caribbeans.
I have to agree with CrazyRu and others that a centerboard on a 'full keel' sailboat is generally a good thing as it does help in pointing ability and other downwind performance issues. What you are calling 'full keel' is more likely a full keel with a cutaway forefoot. 'Full keel' means that there is a full keel from bow to stern.
If your boat is like my Tartan 27' from 1969 which has a centerboard then you should use it. I can basically get our boat to steer itself on some points of wind by adjusting the centerboard angle.
One additional advantage to having a centerboard that pivots down and out of the keel: it moves the center of resistance aft, particularly if the board is about half way out of the centerboard slot. This helps a little if the boat has too much weather helm sailing with the board up.
I have a Creekmore 37 with a "full" keel and a centerboard. The length of the board that is exposed below the keel is 59 inches when the board is down. The board is 22 inches wide. It weighs about 95 lbs so it is not significant in terms of ballast. The centerboard slot is below the main cabin floor.
See exchanges about Creekmore sailboats in the "Living Aboard" Forum.