You can do this. Like others said, if you want to pay for it and said person is willing to hang onto it then your fine. What type ammo are you looking to buy? I buy ammo in NH all time at Walmart. I have thought of doing the same thing. I know a few people that can get ammo shipped to their house.
Honestly for all pistol ammunition (.22LR, 9mm, .40S&W, .38 sepcial, .380, .45, etc.) It was cheaper just to buy WWB from walmart in NH, no tax no shipping. If your buying 7.62x39mm or .223 (5.56) then you can save some money by getting it shipped to someone else in another state.