Is there as way or approach to understand and study the evolution of intrinsically disordered proteins based on their amino acid sequences using phylogenetics?
Any DNA or protein sequence (as well as morphological traits and many other types of data) can be studied using phylogenetic methods. I am not quite sure what you mean by "intrinsically disordered proteins", but many proteins do not take on one rigid 3D structure that is easy to crystalize and understand based on its 3D crystal structure. It is important to understand what level of sequence diversity can be analyzed, and how the proteins (encoded by genes) evolved in the system you are working with. For example studying the evolution of a family of related proteins in one or more species (such as studying GTP-binding regulatory proteins) is a bit different from studying a single-copy protein (such as ribosomal elongation factor 2) in many vertebrate species.
@Brian as correctly mentioned, Intrinsically disordered proteins are those which do not have a defined structure. When such proteins from different species are analyzed and aligned, the resulting alignment shows a poor score since the amino acid residue variations are relatively higher. For instance, I am working on a prokaryotic transmembrane protein and when aligned using PRALIN-TM (specific for TM proteins), I align the same protein from two different groups of bacteria, the alignment has a poor scoring with very little conservation in the disordered region. Similar results are observed with other tools such as CLUSTALW2/O or MUSCLE. How can this be used for phylogenetic analyses. Would the sequence disparity affect the resulting tree?
Even in highly ordered proteins which are overall homologous (homology is sharing a common ancestor) some regions may not be homologous. The percentage of similarity or identity of homologous regions will also be higher in some regions than others, conserved vs variable regions of the protein. Groups of bacteria can be so distant from their shared common ancestor that it can be difficult to determine of some regions of a protein are homologous or not. Salmonella and Escherichia are closely related to each other, but very distant from Clostridia, for example. It is rather common for recombination to swap small regions of DNA so that some parts of a gene are "new" and did not share the same history as the rest of that gene. Phylogeny only works for the parts that shared a common ancestor.
Can be very helpful in pruning out regions of a multiple sequence alignment which are of questionable homology, or may not be correctly aligned. Even if a region is variable or hypervariable rather than truly non-homologous, it can be so far distant (very low similarity) that phylogenetic signal has been lost.
Some proteins are so highly conserved that there is some phylogenetic signal across very vast evolutionary distances. For example some of the ribosomal proteins such as initiation factors and elongation factors can be compared between eubacteria, archaebacteria and eukaryotes. Other proteins loose similarity so quickly that it can be difficult to use that protein to compare amphibians to other tetrapod vertebrates.
Bacteria are very diverse, so comparing one bacterial group to another can involve greater distances than comparing fungi to plants and animals.