I'm not aware (and don't *think*) that it was suspected as a possible hoax, at least in so far as anyone coming out and saying so, and I'm not *aware* of any documentary evidence that anyone privately thought so.
What you are probably getting at, however, is that -- apart from the hoax angle -- many contemporary anthropologists (and I think a majority among leading figures) did correctly interpret Piltdown initially, suggesting that it was a fortuitous association of an ape jaw and a human cranium. IOW they felt that it was not a single individual or species, or at least couldn't be accepted as such on the available evidence.
The hoaxer doctored some of his remaining material and arranged a second find, clearly designed to eliminate these objections. (The second or "Sheffield Park" find was a piece of frontal bone from the left lower eye orbit to the root of the nose, a bit of the occiput, and a molar. This was the same association of human cranial/face and apish jaw. The finder and probable hoaxer Charles Dawson represented it as a second individual of Eoanthropus, but IIRC it was all material left over from creating the initial find.)
John Evangelist Walsh, in Unraveling Piltdown (Random House, 1996) describes the effects of the Sheffield Park find as follows (pg 60) first quoting Arthur Smith Woodward at the scientific meeting where it was described:
... "The occurrence of the same type of frontal bone," he stated pointedly, "with the same type of lower molar in two separate localities adds to the probability that they belonged to one and the same species."In that professional audience, all knew well what Woodward meant by the quiet mention of "probability" in connection with the "two localities." Perhaps it might happen once, accidentally and randomly, that a real ape's jaw should wind up in the same pit alongside a human brain case, both of them fossilized. That sort of accident was admissible, though barely. But the odds against such a chance pairing of opposites, of unrelated but similar artifacts, occurring a second time in the identical vicinity could be said to verge on the mathematically impossible. It was clear that the Sheffield Park finds established the incontestable reality of Piltdown.
Gradually, over the next several months and years, accelerating with the war's end in the fall of 1918, many experts who had vehemently opposed the combination of jaw and cranium now simply gave way, confessing themselves wrong. The conversion, while by no means complete, was dramatic and sweeping, affecting some of the leading names in the field worldwide -- for instance, one of the best-known, Marcellin Boule of France. The reaction of one American anthropologist, long an opponent of linkage, wonderfully illustrates the transposing impact of the new discovery.
In the summer of 1921, Henry Fairfield Osborn, president of the American Museum of Natural History, visited London. [allowed to examine the Piltdown material...] For two uninterrupted hours the skeptical Osborn peered and measured, his comparisons patient and painstaking. Suddenly he found he could no longer hold out.
"If there is a Providence hanging over the affairs of prehistoric men," he said afterward, "it certainly manifested itself in this case." The three small fragments of the second Piltdown man, he marveled, "were exactly those which we should have selected to confirm the comparison with the original type." Just those specimens which were most needed by the advocates of Eoanthropus had actually been found. Inspecting the second Piltdown cache, placed side by side with the corresponding fossils of the first, Osborn was forced to admit that "they agree precisely; there is not a shadow of difference."