It depends what you mean with "information content". The alignment is a hypothesis about site homology, which means that the phylogeny based on this alignment is a way of analyzing and visualizing the underlying pattern. Bootstrap analysis gives an idea about the degree of homoplasy in the data, i.e. the proportion of putatively homologous sites with conflicting information. Evolutionary models used for the analysis take the proportion of bases into account and you can partition the alignment using various criteria based on alignment patterns. Apart from that, you can subject alignments to analysis of alignment confidence. There are even approaches to evaluate homoplasy prior to compute a phylogenetic tree. Most of these and additional methods are usually done in a standard phylogenetic analysis and are also often discussed when interpreting results (at least that would be recommended).

It depends what you mean with "information content". The alignment is a hypothesis about site homology, which means that the phylogeny based on this alignment is a way of analyzing and visualizing the underlying pattern. Bootstrap analysis gives an idea about the degree of homoplasy in the data, i.e. the proportion of putatively homologous sites with conflicting information. Evolutionary models used for the analysis take the proportion of bases into account and you can partition the alignment using various criteria based on alignment patterns. Apart from that, you can subject alignments to analysis of alignment confidence. There are even approaches to evaluate homoplasy prior to compute a phylogenetic tree. Most of these and additional methods are usually done in a standard phylogenetic analysis and are also often discussed when interpreting results (at least that would be recommended).

I fully aggree with Robert Lückings answer

As a hint: Information Content is used for data selection e.g. by MARE (see e.g. Misof et al. (2013) Selecting informative subsets of sparse supermatrices increases the chance to find correct trees BMC Bioinformatics 14: 348

https://www.researchgate.net/publication/259152317_Selecting_informative_subsets_of_sparse_supermatrices_increases_the_chance_to_find_correct_trees?ev=pub_cit_inc

Article Selecting informative subsets of sparse supermatrices increa...

In my personal opinion, data exploration "prior to" phylogenetic analysis is (or should be) necessary. Despite support values given by a particular alignment, results derived from this may be extremely dependent on specific values of the alignment parameters. In other words: "how robust (general) are my results?", "How much dependent on parameters values my result are?". A paper in line with this idea (and perhaps foundational) is that of Wheeler (1995):

http://sysbio.oxfordjournals.org/content/44/3/321.abstract