Can packaged, long-shelf-life foods enter the US via courier service?
Yes. There is probably millions of packages like that around christmas time each year, and it's perfectly normal and legal, all year long.
Are there any specific restrictions on what ingredients may or may not be brought into the country?
Yes, Kinder eggs are banned. It is not allowed to "hide" non edible small parts in food because it is deemed a hazard, and Kinder eggs fit this description to the letter. While as a European I think that's weird, nobody can possibly accidentially swallow the huge yellow capsule inside, the law itself makes sense and is not going anywhere soon. So don't send Überraschungseier specifically. Everything else should be fine.
Make sure you stay under the tax limit for gifts and declare it as a gift. Otherwise the receiver may need to pay more customs fees than the candy is worth. That might still be okay around Christmas, when there is "exotic" stuff and flavors in the box, but for a simple "thank you" candy box, it would be unfortunate.
On a personal note, pick flavors that don't exist over there. "Waldmeister" is a thing most Americans have never heard about, and around Christmas Time, for whatever reason, many candy bars are offered with "Spekulatius" flavor here, but that flavor is never sold in the US. Duplo is a thing they don't really have over there, too.
In case you are sending other gifts too, or just have some spare room in the box: don't use packaging material like styrofoam pellets or recycling paper shreds. Gummy bears can be bought in a big pack that contains lots and lots of mini bags of 5-7 each. Those are perfect packaging material. Stuff the whole box with little gummy bear packages instead of styrofoam balls or paper.