Yes they can have children depending on what other medical issues they may have.
From my readings, there have been new possibilities opened up fro Thalassaemics. Yes, they can have children. Obviously risks will be there.. but those risks are no different from any other normal pregnancies..
If they are in good health.. with proper Hb levels.. proper iron levels... then the problems are lessen.
But one has to see a high risk OBG.. who will work together with your Hematologist...
In regards to the heritary aspect, again this depends on whether you are a minor, intermedia or major.
If they are a minor, then they have a 50% chance of having a baby with Thal trait and a 50% chance of having a baby with no affected genes.
If they have Intermedia or Major then the baby will inherit the gene depending on the parent's severity.
I have based this from only one parent being affected and the other parent being cleared of the gene.
You can check out Thalpal.com
It is a website that has Thalassaemic patients, their friends and families go to ask questions and/or give advice. You will find many topics and disscussions covered that relate to Thalassaemia.

Congradulations to your friend for her up and coming wedding.
I wish her the best.