First, let me congratulate you for getting into tailwheel aircraft!
what counts as tail dragger time?
What counts? Time spent learning to operate a tailwheel plane -- that is, learning the techniques required to taxi without being able to see over the nose, without abusing the brakes and keeping all wheels on the ground in normal and high winds, avoid groundlooping a plane, properly "unsticking" during takeoff, making three-point and wheel landings, avoiding propeller strikes...
At a typical tailwheel conversion course you spend no time away from the circuit, unless you pay extra for it. A tailwheel airplane in the air is just an airplane with less drag than a fixed-nosewheel one. But it becomes a very different thing on the ground, and that takes a little getting used to if you've done all your flying on nosewheelbarrows.
If you have experience with landing non-powered aircraft in a tailwheel configuration some if it may count. It really depends on the kind of experience.
Have fun!