We just published an article making what we feel is a plausible case in favor of an affirmative answer in Foundations of Science, see preprint here. The basic argument is that while such a requirement may seem very limitative, such an embedding seems possible with a small number of additional ingredients like a black box for returing the sum of a series, and I was curious how well-supported this appears and if there are aspects that may have been overlooked.
Crosslisted at HSM without generating much response.
Note. Leibnizian calculus is calculus as it was practiced by Leibniz, in the same sense as Euclidean geometry could be interpreted as geometry as practiced by Euclid (though the term often has a different meaning). An example that we give in the paper of the type of mathematics that would not be Leibnizian calculus is a proof of the extreme value theorem, a 19th century argument.