Sure, strange man could (rarely) mean stranger
In older use, strange man could mean stranger, since strange meant unfamiliar, alien, or unknown. For instance, in a retelling of the story of Huon of Bourdeaux from 1601 (via Early English Books Online), the hero enters a new city and talks to a man he is unfamiliar with. After a few exchanges where he is referred to in pronoun form ("quoth he"), this statement is made:
Sir, (quoth the strange man) séeing it is so, for the loue of God I shall bring you to a lodging, whereas you shalbe well and honestly lodged, in a good mans house that beléeueth in God, named Gonder, he is Prouost of the City, and well beloued with the Duke.
This almost certainly is the equivalent of saying "stranger" - the speaker is a man in a town foreign to the hero who the hero doesn't know. This usage of stranger is common in late medieval and early modern English texts.
Similar usage is less likely now, as strange (adjective) has semantically shifted. It more often refers to someone abnormal or odd. Specific to strange man, stranger would be a more efficient way to refer to someone unknown.
In the rare occasions where strange man is used to refer to a stranger, it feels more emphatic. Here's J. R. Ripley's Buried in Beignets, dug out from over 300 results of strange man referring to an odd fellow:
But even though he was a fellow shop owner, I barely knew the man. I didn't want to be inviting some strange man into my storeroom this early in our relationship.
"Some strange man" seems to be a common form of emphasis when they're a stranger and not abnormal or peculiar. Here's a transcript from a 2015 show Primetime Live, that I found on COCA after fine-tuning my search:
JOHN QUIONES (ABC NEWS) It becomes a family affair when my own son puts his girlfriend to the test. The question? How will these unsuspecting significant others react to an overly flirtatious waiter?
JOHN QUIONES (ABC NEWS) (Voiceover) Remember Tommie?
TOMMIE# Some strange man is flirting with my wife in front of me, and if I wasn't such a nice person I'd (censored by network) I'd stab him with the damn butter knife.
With that additional insight, I can found other examples meaning stranger, including this from Google Books:
Oh, Emily, you talking crazy. You know as well as I do that in this world we live in it's close to suicide to just strike up a conversation with some strange man on the street. (Ugly Ways by Tina McElroy Ansa)
One other detail: the gender of the person is important in all of these present-day cases. A woman is speaking in the first and third cases, suggesting a real risk posed by talking to men who are unknown. In the second case, a man expresses feeling threatened when an unknown man flirts with his wife. So the emphasis in strange man (meaning stranger) seems to be on his gender as much as his unfamiliarity.
That said, note that strange man is much less common than stranger, and some strange man is less common still. So we're discussing a small percentage of cases when strange man is used.