Yes if an american order a product from you, and that product is legal in US, there is no reason why he wouldn't have it shipped in the US, or directly from a US fulfillment service you work with.
I do that all the time. I tested both method (I'm outside US too, I'm in Europe).
In the first case, your customer will have to pay import taxes (and shipping from your to him).
In the second case, you will have to pay import taxes (and shipping from you to the fulfillment service). Your customer will pay from the fulfillment warehouse to him only.
Please note that some products must have exportation AND/OR importation certificates.
One obvious product that needs them is weapons ;)