It would be a syntax error. . . unless you add syntax for it.
As far as it being a bug waiting to happen, C already has plenty of traps like that - '=' vs '==', '&' vs '&&', and so on.
In terms of grammatical clarity, I shouldn't think it would be any more confusing than any other operators that have both unary and binary versions. By my count C already has three of those: '-', '&', '*'. The latter two are even examples where the unary meaning and the binary meaning are wholly unrelated.
Besides, it's a way of using + that is already well-established in everyday idiom. And there are semantically-related uses for + that are already well-established in computer languages, too - the Kleene +, for example, should be familiar to everybody.
In terms of how it would work for the grammar I realize this would be somewhat of a departure since it's repurposing a symbol that's normally an operator to be used in a manner that would be more like a keyword according to C syntax. . . but I think that's a detail that should be much more interesting to standards committees than it is to people who primarily just use the language. And in terms of the human factor I submit that it's much more workable than taking a word from the English language and repurposing it to mean something that's more-or-less the opposite of what it means in English.
I never ever had problems with it in C. I actually had a problem with it in another language (might have been a BASIC) where = was contextual, so one could do "a = 10" and then somewhere down the line "if x = 5 then". I used == and couldn't figure out what was wrong for nearly 5 minutes (I think it was recognising (or not) as an unexpected token).
= and == should have different meanings.