Was American slavery economically advantageous primarily due to being able to also sell offspring?

This would depend upon which America you're looking at, and when. This chart of African slave shipments shows that most Africans taken into slavery went to either the British Caribbean islands or to central and south America. Of the Africans taken into slavery, less than 10% came to the US.

The reason to import slaves was for labor. Thus, the primary source of income derived was from the results of that labor - cotton in the southeast US, sugar cane in the British islands, and gold and silver mines in central/south America.

The raising of young for slavery became a factor in the US after 1808, when the importation of slaves from Africa was banned, but the practice of keeping people in slavery was not.

Certainly, in the case of the Spanish and Portugese running the gold and silver mines, breeding was not a concern - the average life of an African in their mines was one year. The mine owners had calculated that it was cheaper to ship over more, than to provide proper food and shelter for the people already there. Thus, the one year life span - that's how long they lived under those conditions.

That policy explains both the high level of slave importation, and the relatively low number of people of African descent living in central and south America today. They were worked to death before they had a chance to bear children.

There are no exact figures of how many Africans died in the gold and silver mines, but it is thought to be in the 6-8 million range.

Yes. It was (mostly) the Confederate states of America that imported around 300,000 slaves over two and half centuries, and the Confederacy ended up with nearly four million.

Virginia was the clearest example. It was a net exporter (and breeder) of slaves to other southern states because slavery was unprofitable on a standalone basis in that state.

Other such states were Kentucky and Tennessee. It was because of this fact that "sell someone down the [Mississippi] river" became a saying, based on the next paragraph.

It was mainly in the hotter, faster crop-growing "Deep South" states (basically the states that supported Barry Goldwater in 1964, not counting his native Arizona), where slavery was profitable on a standalone basis.

Slaves were considered a capital asset not just labor. By 1861 almost half the total value of the South's capital assets was in the "value of negroes". They were taxable wealth. When slaves were freed the slave owners lost over $2 billion in capital. Most agricultural societies the most valuable asset is land, in the South it was slaves. They bought a lifetime of labor that was portable. Mortgaging slaves was the most common way of raising capital. In antebellum Louisiana 88% of loans secured by mortgages used slaves as collateral. The 13th Amendment ended this.

Good source: "Capitalism in America; An Economic History of the United States" by Alan Greenspan and Adrian Wooldridge

If slavery is only profitable through the selling of slaves, there's no point in having slaves except as a social status symbol (which may be the case for some slaves in some societies, but not for the type of slavery you're talking about.

That alone should show you that the argument is fundamentally flawed.

No, slavery becomes profitable in a society where there is work that requires a lot of manpower (preferably largely unskilled labour) and there are relatively few free people available to do the work, either because the work is highly unpopular and people'd rather go hungry than do it, or because there simply aren't enough people at all. In the early USA this was certainly the case. The land was large and wide, the people were few, society was built to a large degree around agriculture and to some degree mining. As industrial cities started to grow, the demand for agricultural products increased, while the population moved towards the cities for the easier and better paying jobs available there, providing the conditions for slavery to become a viable means of staffing the ever larger farms in a still largely pre-mechanised society.

The influx of Chinese labour you mention only started later, and together with an increased influx of other fortune seekers from other parts of the world eventually created the situation where slavery was no longer profitable, especially when combined with increased mechanisation options.

Even without the civil war (which really wasn't about slavery at all, even though there were indeed many more slaves in the confederate states per citizen than there were in the union) slavery would likely not have lasted all that much longer in the US, it simply stopped to be a viable economic model as cheap, well educated (relatively) labour became more plentiful.

Was American slavery economically advantageous primarily due to being able to also sell offspring?

No, American slavery was economically advantageous regardless of selling offsprings.

If X continuously makes revenue breeding slaves and selling them to Y, we can assume following:

1. Y makes revenue (directly or indirectly) by using slaves bought from X (otherwise Y would stop buy slaves);
2. In average, this revenue made by Y exceeds amount which Y pays to X for the slaves, otherwise Y would stop buy slaves;
3. X can not effectively make revenue by using slaves the same way as Y, otherwise X would stop selling slaves to Y and start to use them himself, making more revenue (see 2).

All these conditions were in effect in US by the middle of XIX century. Let's read and analyze "A Declaration of the Immediate Causes which Induce and Justify the Secession of the State of Mississippi from the Federal Union", second paragraph:

"Our position is thoroughly identified with the institution of slavery-- the greatest material interest of the world. Its labor supplies the product which constitutes by far the largest and most important portions of commerce of the earth. These products are peculiar to the climate verging on the tropical regions, and by an imperious law of nature, none but the black race can bear exposure to the tropical sun. These products have become necessities of the world, and a blow at slavery is a blow at commerce and civilization"

So we have Lower South states (Y), making revenue by producing "product which constitutes by far the largest and most important portions of commerce of the earth" (cotton), using slave labor.

We have Upper South states (X), who can not produce cotton, "peculiar to the climate verging on the tropical regions", as effectively as Lower South (condition 3), but can sell slaves to the Lower South states.

As we can see, American slavery was economically advantageous primarily due to unique ability of the Lower South states (Cotton kingdom) to supply "the product which constitutes by far the largest and most important portions of commerce of the earth". Selling slave offsprings (from Upper to Lower South) can somewhat increase this advantage, but could not be its primary reason.

Speaking about Chinese laborers - this is pointless discussion. By 1860, it was about 35000 Chinese people in US, 100 times less than number of slaves. By 1850 - about 4000, practically none - before 1849 Gold Rush.