It will be much easier for the doc to check your density with short hair, so don't worry about that.
I would actually advise you to get a little USB microscope yourself. They are pretty cheap. I am from the UK and picked one up for £35 from maplins (which is about $55). Some benefits of having your own USB hair density scope include:
1) You can check your own donor density (before and after surgery)
2) You can monitor the minituarization process on the top of your head
3) You can accurately determine if topical/oral treatments are working for you, by looking at hair thickness/density in specific balding areas.
4) You can see your grafts come through from months 3-18 post-op.
5) You can get a good estimate of how much growth you have had post-op. You can take a few areas of 1cm^2 and get an average growth count (grafts/cm^2). I would imagine in the majority of FUE cases, the growth will be less than what was paid for. With the scope, it's easy to differentiate between transplanted hairs and native hair. You can see the inflammation at the root of a transplanted hair and they are obviously significantly thicker than native hair.
6) If you have FUE, then you can see all the scarring post-op (including white dots)
I'm sure there are lots of other benefits that i can't think of right now
Good luck !!