I am a little bit disappointed that they will not issue the license straight away
do not quote me, I might be wrong !
I only did the initial one at Barcelona at clinica Quiron, and it took them 2 weeks to send it to me by post, but it was about 3 years ago. (Had to do the full medical again because I had a french one but it was not "officially" JAR FCL 3, so Spanish DGAC did not want to deliver me my CPL licence without a JAA medical certificate
)
But, I remember some friends of mine did the renewal at Valencia and I think they had to wait also about 2 weeks to get the certificate by post. The thing is that the general doctor hast to send the result to DGAC at Madrid, and then DGAC send you the certificate !.... You know ! ... Spanish administration
Maybe they have changed in the meantime, I don't know.
At least french DGAC and CAA give you the certificate straight away now !
Good luck, and enjoy greek Kebabs !