Bigrams ending in third tone where first syllable is second tone vs. third tone This is regarding tone sandhi for consecutive third tones.

I notice CC-CEDICT has over 200 bigrams with tone pair 3-3 where there also exists a separate bigram 2-3.

One such example is:

白果 bai2 guo3
百果 bai3 guo3


Tone sandhi says that the second should also be pronounced bai2 guo3.

I have two main questions about this:


Are both words pronounced exactly the same?
If no, can a native speaker (listener) consistently distinguish the two words apart from one another?


In general, I'm curious whether tone sandhi is merely an approximation (that the first 3rd tone should be pronounced as a second tone).

As a bonus question, if the words have exactly the same pronunciation, why do dictionaries not standardize so that both words show the same pinyin (e.g. "bai3 guo3")?
There have been conflicting claims on whether the second tone and the "raised third tone" are distinct, but according to Jerry Norman's 1988 book, Chinese, "Perceptual tests done by Dreher and Lee (1966) and Wang and Li (1967) established that native speakers are unable to make a consistent distinction between second tones and raised third tones" (147). So all 2-3 and 3-3 compounds are homophones; the only way to tell which is intended is by context.

[After new edit to question] The question is divided into two parts: 1) Do native speakers actually produce 2-3 and 3-3 pairs in an acoustically distinct way? 2) Can "native listeners" accurately distinguish  between 2-3 and 3-3 pairs when they hear them? 

The studies Norman cites address the problem of the listener, i.e. they are perceptual studies.  I have Wang and Li (1967); I won't try to summarize it, but I think the subjects, the sample, the format of the experiment, and the statistical analysis are good. Wang and Li found that the accuracy with which native listeners distinguished 2-3 and 3-3 pairs "in neutral speech" ranged from 49.2 to 54.2 percent. In other words, they were wrong half the time. This is no better than guessing, so Norman says they are 'unable to distinguish consistently.'

This is the perceptual side, not the production side.  You also want to know if people actually "pronounce" the two differently.  I presume you mean that by using physical measurements we can come up with a consistent set of differences between the two members of each pair.  Wang and Li discuss and reject this idea: 


  Does tone 3 become tone 2 when it occurs before another tone 3?
  Attempts to answer this question have been made by extensive
  measurements of spectrographic data on voice pitch. Such attemps have
  not yielded, and indeed cannot yield, any conclusive results. The
  nature of phonetic variations is such that we would expect to find a
  great deal of overlap in the physical measurements of the two types of
  tone sequences mentioned above.


Putting this in my own words, there is no principled way to decide which of the vast number of acoustic components produced by an individual utterance of a 2-3 and a 3-3 compound people might use to distinguish the two.  We can't look at the signal and pick out what part "means" something. This is a familar problem in linguistics, right? Perceptual tests avoid this problem and produce an objective answer, which is simply that people can't distinguish these pairs.

Let's put it another way. Imagine that native speakers actually produce 2-3 and 3-3 pairs that are "distinct." Distinct here means a physically measurable difference (pitch, loudness, duration, or some combination) that is used consistently in all such pairs, regardless of their otherwise different phonetic/phonemic structure, and can be detected using acoustic instrumentation and/or analysis.  

Forget that we can't do this; suppose we can. Wang and Li have already shown that for some reason, native listeners are not able to detect this distinction at better than 50-50 accuracy.

I think this is at least a paradox, if not a contradiction: do languages have sounds or sound patterns that everyone uses, and are physically different in a consistent way between phonologically "minimal" pairs of different words, but that no one can distinguish? What does it mean for "distinct" words to be "undistinguishable"? Note we are not talking about "performance" issues here.

Wang and Li do consider the problem of making clear which pair you want to express: "It is obviously possible to distinguish the 3-3 sequences by employing various additional features, such as extra stress, pause, etc." This is why the phrase "neutral speech" is added in their description of their results.

Bonus answer: you seem to be asking why the dictionary lists the pronunciation of 百果 as bǎiguǒ instead of báiguǒ.  Most dictionaries give only the 'isolation' tones for single characters, even in compound words.  For example, the Pinyin Chinese-English Dictionary says 'Tonal changes within compound words are not generally marked.' 

There are several reasons not to mark tone sandhi in dictionaries. Convenience is an important one; changing compounds to use sandhi forms is more complicated than just leaving them alone. 

Another reason is that the domain of sandhi rules often crosses word boundaries. Since sandhi occurs whether something is a word or not, a dictionary perhaps need not register such non-lexical changes. 

By the same logic, the morpheme bái 'white' and the morpheme bǎi 'hundred' are phonologically distinct. Although they merge phonetically in some environments, that doesn't mean we should ignore the distinction between the two and give the 'surface' form in dictionary entries where sandhi rules may apply.