It's an unrealistic, idealistic goal, but yes; if 100% of Americans recycled all of their recyclables, used composting, and were all as "green" as they could be; many of the imports would decline.
However, that being said, there are plenty of things that you can't recycle that would still have a need to be imported. There would be a shift in other country production to match whatever demand there is for "exports".
Take goat meat for example. You can't recycle food products. There is a huge import of goat meat to the US from other countries.
I'm not sure why the cost of shipping would go down. You would still be paying the same price per pound to ship things. The tariff taxes would stay the same, there may just be less income from it, due to fewer items being shipped.
Jobs in recycling would increase slightly, however I don't think there would be an equal number of jobs created in the US as jobs lost in other countries over the "switch". It's not cut and dry like 10 Americans got hired to sift through the trash to find recyclable materials so 10 people from somewhere else lost their job...