No, the scheme you described is for Value-Added-Tax countries, the US does not yet have a VAT.
In the US, sales tax is collected on a State-by-State basis. Occasionally, if you buy from a company that does not have presence in the State where the goods are delivered, you would not have to pay sales tax. But most phones are sold by companies that have a presence in every state, and collect the state sales tax in every state that has a sales tax, so that does not work very well for phones.
If you are a US company purchasing goods for resale under certain conditions, you can use your resale identification number to not be charged sales tax. But I expect this would not work for most Apple products.
Idris Seabright is correct that some states do not have a state sales tax. New Hampshire is another state that does not have a sales tax. In some cases, the goods sold by national companies are priced higher in non-sales tax states to keep customers from cheating.