You may indeed.
Well he had a tribal identity, and was clearly an Arab. I.e. An Ishmaelite, I don't think that is under dispute. To say he was a pagan is a bit silly. Judaism and Islam don't really slot sensibly into paganism as they recognise The God of Abraham.
"Then We inspired you: 'Follow the religion of Ibrahim, the upright in Faith'."
(Qur'an 16:123)
Obviously Islam does not understand the religion of Abraham or else they would be Christian.
As Islam forbids idol worship, it may be false witness to say that Mohammed was an idol worshipper.
He was 1000 not 2000 years after Jeremiah. Do some homework