On a technical level PT are usually pretty quick these days in addressing line issues in the Algarve. However, you may well have problems with the bureaucratic process.
There may be another solution depending on your property's geographic location. Forget PT!
Depending on the volume of bandwidth you need each month, Vodafone have now launched a product called BestNet and TMN have a similiar one.
Kanguru Optimus probably have a similiar product but their site is a mess at the moment and it its difficult to ascertain package options..
This gives you broadband access over the mobile phone system. No phone line is required.
You could perhaps them make do with a mobile phone for voice calls and have broadband using the above system. I would suggest that you take the account out in your personal name.
Vodafone Broadband Tariff Details (in Portuguese) here:
TMN Broadband Tariff Details (in Portuguese) here:
However, I really do strongly recommend that you get a site test done at the property before going down this road to ensure that you can receive a stable 3G signal within the property and therefore receive the maximum speed available.