Quote from Aaron:
The discount to spot is a function of long rates minus short rates. The long rate or yield on a long bond is a combination of the coupon and the amortization of the discount or premium versus par. So, in short, I think the answer to your question is "yes".
Buying long bond futures is just one version of the carry trade. Like you say, you might want the version where you buy mortgage bonds (agencies) instead. Or maybe you want to buy foreign bonds, or corporates, or munis, or an off the run Treasury (like Egotrader said), or whatever.
Some hedge funds might also stick with the cash market because futures contracts are under CFTC jurisdication and the fund might not want to deal with the additional compliance issues.
Here's another version of the carry trade a retail investor could do: In your brokerage account buy high yielding preferred stock, stock, or REIT's on margin. As always, the defining characteristic of a carry trade is that you are borrowing at short term rates and investing in a longer duration instrument to get a higher yield.