The hash table is O(1) even without your modification. Because there is a fixed dictionary, the length of the longest possible word is known in advance. That provides a constant bounds that does not grow. Let's say the longest word is 25 letters. Your hash computation is O(25) which is equivalent to O(1).

What this means in practice is that there is no polynomial curve for very long words. You don't bother hashing them, so the curve peaks and then flattens.

Obviously a trie is an interesting and possibly faster solution, though the hash has the benefit of being more cache friendly. But the big O analysis presented for this problem is flawed.