There isn't just a single pronunciation of Latin in use, there are many. You can say /ˈgrae̯kae̯/, but whether you "should" is a matter of opinion.
The transcription [ae̯] is one way of representing a reconstructed pronunciation of Latin "ae". (A very similar transcription would be [aɪ̯]. English students of Latin are commonly told to use the diphthong found in English words like "price" for Latin "ae".) For various reasons, like etymology and sources that seem to indicate distinctions in pronunciation between "ae" and "e", it is thought that the pronunciation of "ae" passed through this stage, but it wasn't always pronounced that way.
The pronunciation before [ae̯] or [aɪ̯] is thought to have been [ai̯] or [aj].
The pronunciation after [ae̯] is thought to have been [ɛː]. The value [ɛ] can be reconstructed from Romance reflexes, and [ɛ], or a similar sound like [e], exists as a pronunciation of "ae" in most traditions of pronouncing Latin that have come down to the present era (for example, the so-called "Ecclesiastical" pronunciation).
The use of monophthongal pronunciations like [ɛ(ː)] typically goes along with the use of a fronted and affricated pronunciation of "c" before "ae", "e", "i", "oe" and "y". The "Ecclesiastical" pronunciation of Graecae would be something like [ˈgrɛːt͡ʃɛ]. (The vowels might be a bit variable: note that Italian, the main influence on Ecclesiastical pronunciation, does not have a phonemic distinction between "short" and "long" vowels, but uses long vowels predictably in certain phonetic contexts; Italian also only distinguishes between [e] and [ɛ] in certain accents and only in stressed syllables. So a phonemic transcription of the Ecclesiastical pronunciation could potentially be something like /ˈgret͡ʃe/.) Other regional "traditional" pronunciations of Latin are now rarely used, but e.g. a conventional non-reconstructed German pronunciation would be /ˈgrɛːt͡sɛː/ and a conventional "traditional English" pronunciation would be /ˈgriːsiː/.
