Yes, [sɐwˈðaðɨ] is how the Portuguese pronounce the word. The [ɐ] is like the last a in samba as pronounced by both Brazilians and Portuguese: /’sɐ̃bɐ/. You can hear samba and saudade pronounced in Forvo; the first Portuguese on the list (Onimo) is not a good example, but the others are. And [ð] is pretty much like th in the word then.
This pronunciation of d is not particular to the word saudade: in European Portuguese the d is pronounced [d] as in English dare after pauses and nasal sounds, and [ð] as in English there (American version in OLD) otherwise. This pronunciation of the d may be shared by some Brazilian speakers, namely in the Northeast (I think this guy does it), but most Brazilians will always pronounce it [d].
However a Brazilian and a Portuguese talking to each other will likely not notice these differences. But a native English-speaking bystander might. In English [d] and [ð] are distinctive: it is for instance how English speakers tell dare from there in speech. But there is no such pair of words in Portuguese. Many Portuguese may have not realised they pronounce the d differently depending on whether it comes after a pause or nasal sound or not. In fact, in European Portuguese the same word may be pronounced with a [d] or a [ð] depending on what comes before it:
Dada a situação → [’daðɐ]…
E dada a situação → [i ‘ðaðɐ]…
b and g (as in gato) follow the same pattern. This “softening” of the b, d, and g is called lenition and has been discussed in this question.
The [ɐw] European Portuguese pronunciation is peculiar indeed. In European Portuguese the unstressed single a is usually pronounced [ɐ], but the diphthong au is usually pronounced [aw], as in Brazil, even if unstressed, as in caução, laureado, ou tauromaquia. Saudade may be the only word where au is pronounced [ɐw].
And this leads to one last point. Even ignoring accent differences, there actually are two pronunciations of saudade: the first bit, sau can be pronounced as a diphthong, as shown in Wikipédia, or as two syllables [sɐ.wu] or [sa.wu], in which case [ɐ] is the usual pronunciation in European Portuguese, as in saúde, saudinha, saudoso, etc. The 1943 Portuguese-Brazilian agreement (point XII-12º) actually allows the spelling saüdade to indicate this pronunciation. This trema was soon abolished in Portugal in 1945, and in Brazil in 1971. But two syllables may even have been the original pronunciation. My 1939 Cândido de Figueiredo dictionary shows saüdade only; the 1913 edition has saudade, but shows the pronunciation as sa-u.
If two syllabes was indeed the original pronunciation, it would explain the peculiar [ɐw] European Portuguese pronunciation: in Portugal the two syllables are typically pronounced [sɐ.wu]; when the two syllables contract into a diphtong the [ɐ] is kept, yielding [ɐw].
Now as to the meaning and connotations of saudade, I fully agree. In my experience, saudade covers a wide spectrum of feeling on the intensity, tragic-sweet, and poetic-prosaic, scales. Compare the saudade a mother feels a dead child to the saudade you feel for a friend you haven’t seen for a long time but are about to see again, to saudade for eating grape fruit. But I find that many people writing about saudade tend to be biased towards the tragic-poetic end of the spectrums. That Wikipedia quote is one such example. Tchrist’s answer to this question is another.
I've also written on the subject in this thread in ELU, in an answer and comments to Silenus' answer.
