Have you decided on how long you want to tour for?
Are you a seasoned bike tourist?
I do not have ant specific numbers, but believe that A) It might be difficult to find a rental bike that would easily fit into your criteria for a touring bike.
B) Probably would not take very long before the rental bike will be expensive. C) Super big hassle piecing together a touring bike overseas, I like to be able to hit the ground all set up, as apposed to the stress of "putting something together".
I have seen some you tube videos, where they say camping in Portugal is fine.
I went to Italy with a boxed touring bike this spring. Let me know if you have other question(s).