Seeing how industrial the USA is today, is it possible to keep or turn the USA into a agrarian society for more than hundred years? And if so, what could the changes be to the world as a whole (without such a major power, the world would be changed in someway).
Short answer: impossible
Lets see you are talking of:
1) No New England as part of the United States. By the 18th century this region alone gathered most of the shipbuilding, commerce and early industrial output of the 13 colonies.
2) No industrial development (really?, in the middle of the Industrial Revolution)
3) Cash crops and agricultural exportation colonies with cotton, grains, coffee and tobacco as the main source of revenue. It looks a lot like South America in the 1810s.
4) with lots of cotton you can converted in products with added value such as clothes and fabrics. No way to stop mechanized mills and the added value and demand they provide.
4) Even if they reverted from freedom of commerce to a heavy tariff protection to hinder the importation of industrial goods they would still need to provide themselves with them for basics things. For example to ship and transport of goods cheaply.