First off I do not have any knowledge about early black homesteaders one way or the other. But as you correctly pointed out one needed to be a citizen (or a foreigner intending to become a citizen) to qualify. The question of whether freed blacks were citizens at the time is a bit complicated.

The Supreme Court ruled in Dred Scott case in 1857 that blacks were not and never could be citizens. However, many Republicans didn't find Chief Justice Taney's arguments persuasive and felt that anything beyond declaring that Scott wasn't a citizen of Missouri and thus the Supreme Court lacked jurisdiction was mere dicta (i.e. an opinion). It isn't something that immediately stands out, but if you read Lincoln's First Inaugural in 1861 when he calls for stronger protections to ensure free blacks aren't wrongfully enslaved by the Fugitive Slave Law he says:

"In any law upon this subject ought not all the safeguards of liberty known in civilized and humane jurisprudence to be introduced, so that a free man be not in any case surrendered as a slave? And might it not be well at the same time to provide by law for the enforcement of that clause in the Constitution which guarantees that "the citizens of each State shall be entitled to all privileges and immunities of citizens in the several States"?

You can see here that Lincoln assumes a state can make a black man a citizen. Quite a different perspective on black citizenship than Taney's.

In November, 1862. Attorney General Edward Bates gave a legal opinion to Treasury Secretary Salmon Chase. Chase relayed a question from a subordinate "Are colored men citizens of the United States, and therefore competent to command American vessels?" Bates replied after a long treatise on citizenship that "I give it as my opinion that the free man of color mentioned in your letter, if born in the United States is a citizen of the United States" In later correspondence Bates clarifies that even a freed slave if born in the United States is a citizenship.

Now this opinion was in November 1862 which postdates the passage of the Homestead Act in May 1862. But Bates' opinion doesn't create black citizenship, it recognizes preexisting black citizenship. Bates is one of the more conservatives Republicans at the time and so if Bates recognizes black citizenship, then many of the Republicans (though not the Democrats) who passed the Homestead Act could have envisioned that blacks were eligible. But again I don't know how this was put into execution by the General Land Office.

In 1866, Congress passes a Civil Rights Act that provides "That all persons born in the United States and not subject to any foreign power, excluding Indians not taxed, are hereby declared to be citizens of the United States; and such citizens, of every race and color, without regard to any previous condition of slavery or involuntary servitude, except as a punishment for crime whereof the party shall have been duly convicted, shall have the same right, in every State and Territory in the United States, to make and enforce contracts, to sue, be parties, and give evidence, inherit, purchase, lease, sell, hold, and convey real and personal property, and to full and equal benefit of all laws and proceedings for the security of person and property, as is enjoyed by white citizens, and shall be subject to like punishment, pains, and penalties, and to none other, any law, statute, ordinance, regulation, or custom, to the contrary notwithstanding."

And finally in 1868, Congress passed and the states ratified the 14th amendment further securing black citizenship. This was considered necessary because of lingering doubts over whether Congress had the power to pass the Civil Rights Act of 1866 as well as to ensure a permanency that mere legislation wouldn't have.

Sources:

Opinion of Attorney General Bates on Citizenship https://archive.org/stream/opinionattorney01bategoog/opinionattorney01bategoog_djvu.txt

Emancipation -- Then What? by Michael Vorenberg http://opinionator.blogs.nytimes.com/2013/01/15/emancipation-then-what/?_r=0

Final Freedom: The Civil War, the Abolition of Slavery, and the Thirteenth Amendment by Michael Vorenberg

A New Birth of Freedom: The Republican Party and the Freedmen's Rights, 1861-1866 by Herman Belz

Lincoln's First Inagural http://avalon.law.yale.edu/19th_century/lincoln1.asp

Constitutionalism in the Approach and Aftermath of the Civil War by Paul D. Moreno and Johnathan O'Neill