If ambiguity is what the question is most concerned with, I think the short answer to the question is no: distinct structural analyses of an utterance almost always point to distinct meanings.
There are, however, numerous sources of ambiguity, syntax being one and lexical meaning being another. If the grammar does not have a way of acknowledging the cues that disambiguate the utterance at hand, an incorrect structural analysis is easily possible. Consider the following sentence in this regard:
We like the baby in the crib.
This sentence might mean that there are two babies, one in the crib and one on the floor, and we like the one in the crib, not the one on the floor, or it could mean that we like to keep the baby in the crib as opposed to, say, on the floor. The difference in meaning is captured in the syntax in terms of whether in the crib is a dependent of baby or of like. A second example:
a Peruvian silver tray
This noun phrase might mean that the tray is made of Peruvian silver, or it could mean that they tray is Peruvian, whereby the silver may or may not be Peruvian. The ambiguity is again captured in the syntax in terms of whether Peruvian is a dependent of silver or of tray.
Conventional grammar is going to fail to produce a plausible structural analysis of these cases if it does not have a means of disambiguating the meaning. The cues that are important for disambiguation are usually present in context, but if the grammar does not have a way to register these cues, the danger of producing the wrong syntactic analysis is great.
In the case of a Peruvian silver tray, the disambiguation cue comes in the form of intonation. If the phrasal accent is on Peruvian, i.e. a PeRUvian silver tray, the tray is made of Peruvian silver, but if the accent is on silver, i.e. a Peruvian SILver tray, the tray is Peruvian. Concerning the first example, i.e. We like the baby in the crib, I am not aware of an intonational cue that disambiguates the utterance. I assume, rather, that the general meaning context would disambiguate the utterance, e.g. whether or not there is more than one baby in the discourse situation.
So again, if the grammar being used does not have a means of acknowledging these cues, it will often produce an incorrect syntactic analysis.
A similar situation obtains for lexical ambiguity, e.g.
I am blue today.
This sentence could mean that I am wearing blue today, or more likely, it means that I feel sad today. This ambiguity resides completely with the meaning of blue; it is therefore not in the syntactic structure, since both meanings have the same syntax; blue is an adjective in both cases. The disambiguation cue is present in the context of utterance. If I am standing in front of you wearing blue, then it is clear which meaning is intended. Syntax, however, has little to do with such cases.
All that said, there are in fact certain cases in which two underlying syntactic structures are assumed for one and the same unambiguous phrase. This has been proposed for certain noun phrases, e.g. the old fish with stripes. Such noun phrases behave in a unique way with respect to diagnostics for constituent structure, and this has motivated some to propose that there are in fact two distinct underlying structures for such prases. In my view however, that sort of approach is a cop out. One might as well throw up one's hands and declare that one has no idea what is behind the confusing results delivered by the diagonostics.