This is a very tricky question to answer, primarily because this is an entirely different world than the world depicted in Harper Lee's To Kill a Mockingbird. In the 1930s in the South, for example, women were not allowed to be part of a jury, something that seems rather outrageous today. Even worse, of course, was the relationship between blacks and whites. Racism was rampant and a black man (or woman, in the case of different kinds of crimes) was always presumed to be guilty, and a white person's word was always believed over a black man's.
The direct answer to your question has to be no, it would not be true to say that many people would suspect the truth about Mayella's supposed rape because there were not many who would have been willing or able to put reason and logic ahead of their long-held personal prejudices.
One of the key words, it seems to me, is "many." If there had, indeed, been many who were willing to ignore color and look at the facts, it is likely that there would have been more than one of them on the jury. Instead, we know that only one man, Walter Cunningham's father, believed that Tom Robinson was innocent--and even he eventually capitulated to the pressure of the others. If there would have been many in town who were willing to ignore skin color and prejudice, there would have been more demonstrable evidence of support for Tom. Instead we hear very little outcry or anguish over an innocent man being convicted. There are a few voices of reason and compassion, but they certainly cannot be described as "many."
The second key word is "suspect." Even if the majority did "suspect" the truth, they were unwilling to act on it. Because a man's life is at stake, any suspicions should have favored the defendant, Tom Robinson; however, that clearly did not happen.
We do see a little hope in this novel that things are beginning to change, but it is not much and it is not obvious. Atticus, of course, is concerned about guilt and innocence rather than color. The same is true of Judge Taylor, Miss Maudie, the Finch children, Dill, Link Deas, Dolphus Raymond, and even the conflicted B.B. Underwood. We suspect there are a few more sympathetic characters, but certainly not many, and of course the black community is praying there will be many more. Contrast this with everyone else in town who treats this court case as a spectacle and a foregone conclusion, and these cannot be defined as "many."
In his closing arguments, Atticus pleads with the jury by reminding them that "the assumption--the evil assumption--that all Negroes lie, that all Negroes are basically immoral beings, that all Negro men are not to be trusted around our women" is a lie. He says:
You know the truth, and the truth is this: some Negroes lie, some Negroes are immoral, some Negro men are not to be trusted around women-black or white. But this is a truth that applies to the human race and to no particular race of men.
He speaks the truth, and eleven of the twelve men who represent the collective views of the town ignore that truth.
What is a more true statement, then, is that "many" may have suspected the truth, but we have virtually no evidence of it because they were not willing to act on what they knew to be true, even to save a man's life.