Were American slaves allowed to smoke?

The short answer is yes, smoking was relatively widespread among slaves in the Americas from relatively early on (tobacco farming having predated the introduction of slavery to the Americas). Physical evidence for this comes in the form of the remains of numerous tobacco pipes in archaeological digs associated with the remains of slaves and slave quarters; as reported in Slavery in the age of reason : archaeology at a New England farm and The old village and the great house : an archaeological and historical examination of Drax Hall Plantation, St. Ann's Bay, Jamaica. There are also numerous surviving narratives by slaves or former slaves, as recorded in African American slave narratives : an anthology. Volume 1; one such example including an anecdote by the former slave Lunceford Lane in 1845 (p95):

My father suggested a mode of preparing smoking tobacco, different from any then or since employed. It had the double advantage of giving the tobacco a peculiarly pleasant flavor, and of enabling me to manufacture a good article out of a very indifferent material. I improved somewhat upon his suggestion, and commenced themanufacture, doing, as I have before said, all my work in the night. The tobacco I put up in papers of about a quarter of a pound each, and sold them at fifteen cents. but the tobacco could not be smoked without a pipe, and as I had given the former a flavor peculiarly grateful, it occurred to me that I might so construct a pipe as to cool the smoke in passing through it, and thus meet the wishes of those who are more fond of smoke than heat. This I effected by means of a red, which grows plentifully in that region: I made a passage through the reed with a hot wire, polished it, and attached a clay pipe to the end, so that the smoke should be cooled inf lowing through the stem, like whiskey or rum in passing from the boiler through the worm of the still. These pipes I sold at ten cents a-piece. In the early part of the night I would sell my tobacco and pipes, and manufacture them in the latter part. As the Legisslature sat in Raleigh every year, I sold these articles considerably to the members, so that I became known not only in the city, but in many parts of the State, as a tobacconist.

Tobacco use among slaves was not limited to pipe-smoking, of course; that's just the form more apt to leave artifacts for archaeologists. As to your second question:

Would slaveowners allow this or would they see it as a waste of money?

We know many slaves used tobacco; individual regulations, prohibitions, etc. appear to have varied from place to place. At least some slaves were prohibited from or permitted to grow tobacco on their own small plots, according to The Slaves' economy : independent production by slaves in the Americas; from p174:

Masters who did allow their slaves to cultivate tobacco usually required that it be sold to them. Catlett Conway, for example, purchased over 300 pounds of tobacco from seven of his slaves in 1840. William Daniel bought several hundred pounds of tobacco in 1852 from his own and from his neighbours' slaves.

Also, what about hemp?

Hemp was another agricultural industry in the Americas which used slave labor, and some slave use of cannabis is recorded. A history of the hemp industry in Kentucky mentions on p.x:

Soon after World War II the Federal Bureau of Investigation appealed to the Department of History at the University of Kentucky to supply possible information about the smoking of hemp blooms and leaves in earlier years. There seemed to have been some on the parts of slaves, and later field laborers. A case of a slave smoking hemp in the neighborhood of Owensboro could be documented, but there was a vagueness about other instances.

I'm going to quote from another book, but with a caveat; Hemp: American history revisited : the plant with a divided history is more than a bit biased towards pro-marijuana use, and some of its claims regarding marijuana use by historical figures, and the affects of such, are questionable. However, this particular passage from pages 29-30 seem relevant to your question - or at least is part of the question I want to discuss - just take it with a few large grains of salt:

It is also worth nothing that while slaves rarely had access to alcohol, they did have access to hemp; and they had knowledge of the intoxicating properties and medicinal properties of Cannabis. They brought that knowledge with them from Africa, and easily recognized the unique leaves of the plant they knew as "dada." Actually, the use of marijuana as an intoxicant was a well-established practice long before the white man ever discovered Africa, and the Africans probably used it as commonly and as long as their Arab neighbors have used hashish - another form of the same intoxicant. African women reportedly smoked it to stupefy themselves during childbirth. They would grind the seeds into a mush (gruel) that they used to wean children on, and they made it into bread. African tribes historically treated anti-social behavior by forcing the transgressor to ingest large quantities of marijuana smoke; they had an almost nonexistent repeat rate. South African mine owners even supplied "dada" to their workers because it helped them work harder with less fatigue. That situation dramatically stopped after the Boer War, when the British took control--the British saw the use of "dada" by the blacks as a threat to their supremacy. Undoubtedly, the African slaves passed that knowledge on to American-born slaves, but rarely to white Americans, whom they distrusted and rarely spoke to.

No sources, of course, and a lot of this is apocryphal - but it is true that hemp was used recreationally in Africa, but it varied considerably from place to place, and the traditions of its use in western Africa, from where the bulk of slaves were taken, are probably different from those in South Africa. It's also curious you see some very similar stories or explanations given of recreational drug use among slaves, with regards to tobacco and marijuana, as a means of slaves working longer/harder/to sustain themselves against hunger/etc. For example, in Smoke signals : a social history of marijuana : medical, recreational, and scientific there's a claim about hemp plantations in Brazil on p.15:

Black slaves seemed to handle the heat and fieldwork better when they smoked the fragrant herb, so Portuguese plantation owners allowed them to grow cannabis between rows of sugarcane.

Recreational marijuana use is a politically-charged subject, especially with racial overtones on its use, so maybe it's less surprising that these sort of narratives are apocryphal - but as with tobacco there, is archaeological and historical evidence to support hemp production in the Americas, and the use of slave labor in that industry; recreational use of hemp would not be terribly surprising, even if documentation is a bit thin.