Yiannis Tsiolis’ answer nails it:
There are three “components” in to verbalising a language. One is the correct pronounsiaton of vowels and consonants, the other is the correct intonation but the most important is how well you know the language (vocabulary, grammar, syntax, catchphrases). Unless one can copy all three there is hardly a chance he/she will be mistaken for a local.
To the question comments, I’ll add that having a lot of Greek loans and a /θ/ is not going to be enough for even the first component. Yes, θ is a cross-linguistically rare sound. But how does Brazilian Portuguese prepare you for [x, ɣ, ð]? How does it prepare you for the allophony of [k, ɡ, x, ɣ] and [c, ɟ, ç, ʝ]? How does it prepare you for where to use [n] and where to use [ɲ]? (Something there’s real variation on between Greek dialects—as anyone from Patras knows, who has had the misfortune to be made fun of it over.)
Brazilians are not intrinsically better or worse off for learning how to pronounce Greek phonemes natively; I think Spaniards have a bit of an advantage, because of the substantial overlap in their phonemic inventory with Greek, and the rat-tat-tat of their lack of vowel quantity; but they’re also the ones who will be tripped up by [x] vs [ç]. As with any language, you’re going to have a bit of an accent, unless you’re immersed for a long time and you have a good ear. (I know that’s insensitive of me to say, Gustavo, but there’s no way around it.)
But having a bit of an accent is far from the end of the world. After all, it’s not like they won’t know you’re “not from around here”; and it’s not like they won’t truly appreciate you making the effort to learn Modern Greek. Not many do.