Oh boy, this question is a literal mine field (I'm sure it was unintentional, OP) - because the claims made on the matter throughout the Internet are often very speculative. As such, each claim comes with important caveats.

I'm going to go through the verified claims to be "the earliest-born human captured on film" first, then the unverified and contestable ones (by the definition of your question). Onto the verified claims then:

Rebecca Clarke, who was born in 1804 and appeared in "Rebecca Clarke and kitten", is almost certainly the earliest-born. I'm saying "almost certainly" because that film is not easily accesible, but a still from the film is present in Anthony's "The Kinora. Motion pictures for the home 1896–1914" (1996).

If Rebecca's claim is taken out of the question, then the earliest-born human to be filmed would be Pope Leo XIII, who was born in 1810. So, the answer, using only verified footage, would be "No, there were no people born in the 1700s who were clearly captured on film".

As for unverified / contestable claims:

First, Hiram Cronk, the last War of 1812 veteran, got his funeral caught on film. He was born in 1800 - 4 years before Rebecca and on the very last year of the 18th century. However - one could argue if Mr. Cronk counts, since he's dead in the footage, and your question heavily implies living people born pre-1801.

Another claim springs up [in this Wikipedia discussion.] (http://en.wikipedia.org/wiki/Wikipedia:Reference_desk/Archives/Humanities/2009_January_19#Earliest_film_of_the_oldest_person) One person notes that two elderly survivors of the French invasion of Russia were supposedly included in the Russian film "1812" (made in 1912). That statement is not backed up elsewhere, and the image provided seems to be lost (or at least, I couldn't access it properly). Here is the film in question.

Interestingly, Cornelius Vanderbilt has his own IMDB page,. He appears in "Archived footage" on a 1995 documentary - but he died in 1877, while the first motion picture was filmed in 1888. As such, this claim is also open to debate (here on the definition of "Footage" that IMDB uses).

So, hopefully this is an satisfactory answer to your question, OP.