hey
if i were u, i certainly would retake the GMAT and apply if i thought i could do better...
U hav a good gpa, internships ( the fact that it is in france will work to your advantage), a degree from the reputed bocconi.... coupled with a good gmat score, i would certainly say u hav a good chance for HEC...
will ur chances for admission in the last round be diminished is anybody's guess in this case.... The SAI doesn't release applicant data so we have no way of knowing, but i can take a guess....
The following is my theory and feel free to contradict it....
The SAI admission process has 3 rounds... 1st round for gmat scores above 700 and the remaining rounds for any gmat score
I assume that most of those who are interested in applying will have written the GMAt before R1.... Now since all of the applicants who have 700+ scores will apply in R1, the rest of the rounds will have scores below it for the most part. Indeed a large number of places will have been filled in R1 itself given the importance attached to the GMAt score, but there still will be several vacant spots.
Assuming that a majority of applicants in R2 and R3 have below 700 in gmat, if u were to walk in with a 700+ score along with that good profile of urs, i am sure u have a good chance....
But it depends on whether u are very confident of scoring far higher than 640... if not, waiting for the next round is futile