In some specific cases the answer is yes, in other cases the answer is maybe. SHA-3 has four flavors 224, 256, 384, and 512. Now the “block length” given a particular version is 1152, 1088, 832, and 576 bits respectively. Block length is in quotes because this is only the first step in message pre-processing.
All this means is that given the particular variation of SHA-3 that is being processed, the input message will be broken down into 1152, 1088, 832 or 576 bit chunks. Keep in mind this step is completed before any padding actually occurs so the last chuck doesn’t necessarily have to be one of previously mentioned lengths.
Now you have a_set_of_bit_strings, and we’re interested in the last location, or a_set_of_bit_strings[-1] as per python’s notation. At this particular location if the length of the bit string is not one of the following values 1152, 1088, 832 or 576 it will be padded to one of those lengths as outline in FIPS 202.
Next based on the particular SHA-3 implementation all bit strings contained in a_set_of_bit_strings will be back appended with zeros until their length is 1600 bits as per the width specified in FIPS 202. For the purpose of my explanation I DON’T consider this step padding, because it’s not variable based on input message length. People like to use "sponge" to describe this, but I feel it just adds confusion (I don't mean the crypto definition, I mean it's just misinformation). It just means that over each iteration of SHA-3 security(ie collision resistance) is achieved through bits that aren't included in each "block", because in reality the XOR operation can be manipulated to shift all leading bits to either 1 or 0, but you have no control over tailing bits. Hence the strongest version SHA-3(512) splits the message input into the least number of bit chunks!
Things get interesting when the message you’re trying to hash has a bit length that is an integer multiple of one of the following values 1152, 1088, 832 or 576. In this particular situation no padding occurs, and instead an empty string is appended to the end of your message. Why this happens you can determine for yourself. It’s also important to note that this empty string is then passed to the padding protocol outline in FIPS 202. So to answer your question if the bit length of your message is an integer multiple of 1152, 1088, 832 or 576, and matches with its respective SHA-3 implementation, then yes, if you hand me a_set_of_bit_strings[-1] and it’s equal to ‘’ (An empty string) then I’ll know the input message’s length is an integer multiple of 1152, 1088, 832 or 576. But this is a very specific situation. Past this I have not investigated.
I’ve included my SHA-3 bit orientated code below, it’s gross and hacky but it might help you see what’s happening at the end points. The function you’d be interested in would be sb(), and should investigate value set_main[-1] in sb() . If you want to check it against other open source implementations use online_convert().
Link to SHA-3 Code
I will investigate values that aren’t multiples of 1152, 1088, 832 or 576.