What is a phospho-protein binding domain?
This is a very large topic but I will try to partially provide an answer. Now your question has three parts as far as I understand it.


Do phospho-protein binding domains only bind to phosphorylated proteins i.e. is that their sole (observed) function.
What roles do phospho-protein binding domains mediate.
Function of BRCA1 phosphorylation/phospho-protein binding


Just to get some basics out of the way, there are three amino-acid residues in a protein that can become post-translationally modified by phosphorylation, including serine, threonine and tyrosine. Now the purpose of protein phosphorylation ranges from activation/deactivation signals to binding and changing cellular localisation i.e. recruiting a protein to different part of a cell. Now tyrosine phosphorylation, which I know by far the most about is capable of all the above. So if you think about a receptor tyrosine kinase (RTK) such as epidermal growth factor receptor (EGFR), once a ligand such as EGF binds to it, it becomes tyrosine phosphorylated (activated) through its intrinsic tyrosine kinase activity. Once tyrosine phosphorylated, many proteins are capable of binding to tyrosine-phosphorylated RTKs such as Grb2 to induce a signal downstream of RTKs. So as you can see, phosphorylation of RTK affected cellular localisation of GRB2. Excellent Ras signalling review by Karnoub &amp; Weinberg, 2008 Nature reviews (Fig 5). Grb2 binds to phospho-RTKs through a specific domain called Src-homology 2 (SH2) domain, which provides a platform for other proteins such as Son of sevenless (SOS) which is a GEF to bind to it and induce RTK signalling through Ras. So in the above case the role of phospho-protein binding domain (SH2) is to change cellular localisation of multiple proteins and mediate signalling.

Now I'm no expert in BRCA1 but just had a quick look and it seems serine phosphorylation of BRCA1 may be responsible for its recruitment to the DNA site of damage and if serine residues in BRCA1 are mutated, the protein will no longer get phosphorylated, which may effect its recruitment to the DNA sites of damage, which may affect its DNA damage response function (Clark et al 2012 Comput Struct Biotechnol J). Now BRCA has a phospho-protein binding domain called BRCT, and that is also thought to mediate DNA binding and binds to phosphorylated and non-phosphorylated proteins. So BRCA1 phosphorylation and phospho-protein binding is though to be important in its function (Clark et al 2012 Comput Struct Biotechnol J). So to answer your question in short, phospho-protein binding domains such as BRCT do not necessarily bind to their target proteins through phosphorylation.

Hope this helps.