"According to Theravadan Buddhism would the Buddha have been considered an arahant?"
IN SN 22:58 we read the Buddha saying:
"The Tathagata, the Arahant, the Perfectly Enlightened One [...]"
Describing himself as an Arahant, he proceeds:
"What is the distinction, what is the disparity, what is the difference between the Tathagata, the Arahant, the Perfectly Enlightened One, and a bhikkhu liberated by wisdom? [...] The Tathagata, bhikkhus, is the originator of the path unarisen before, the producer of the path unproduced before, the declarer of the path undeclared before. He is the knower of the path, the discoverer of the path, the one skilled in the path"
There are other characteristics of a Buddha. In MN 115 (*) he declares:
It is impossible that two rightfully Enlightened Ones should be born in the same world element at one and same time. [...] It is impossible that a woman should be the perfect rightfully Enlightened One. [...] It is possible that a man should be the perfect rightfully Enlightened One.
Also, MN 12 describes the ten powers of a Buddha (I don't believe these always apply to arahants):
(1) "Here, the Tathāgata understands as it actually is the possible as possible and the impossible as impossible."
(2) "Again, the Tathāgata understands as it actually is the results of actions undertaken, past, future, and present, by way of possibilities and causes."
(3) "Again, the Tathāgata understands as it actually is the ways leading to all destinations."
(4) "Again, the Tathāgata understands as it actually is the world with its many and different elements."
(5) "Again, the Tathāgata understands as it actually is how beings have different inclinations."
(6) "Again, the Tathāgata understands as it actually is the disposition of the faculties of other beings, other persons."
(7) "Again, the Tathāgata understands as it actually is the defilement, the cleansing, and the emergence in regard to the jhānas, liberations, concentrations, and attainments."
(8) "Again, the Tathāgata recollects his manifold past lives, that is, one birth, two births... Thus with their aspects and particulars he recollects his manifold past lives."
(9) "Again, with the divine eye, which is purified and surpasses the human, the Tathāgata sees beings passing away and reappearing, inferior and superior, fair and ugly, fortunate and unfortunate... and he understands how beings pass on according to their actions."
(10) "Again, by realizing for himself with direct knowledge, the Tathāgata here and now enters upon and abides in the deliverance of mind and deliverance by wisdom that are taintless with the destruction of the taints."
"My understanding was that once someone was an arahant then that was it, they had done what needed to be done. He/she was enlightened and therefore at the exact same level of attainment as the Buddha. Is that correct?"
Yes. The difference, it seems, is not of attainment, but of role and skills. Many suttas depict the different skills of arahants, sometimes in contrast with Bhudda's skills.
Ven. Bhikkhu Bodhi develops this further on:
(*) While this excerpt exemplifies distinct characteristics of Buddhas, its important to note that the portion about the impossibility of a woman to become a Buddha is absent in the agama version of this sutta. See Analayo's paper The Bahudhātuka-sutta and its Parallels On Women’s Inabilities and related Q&A here