Could detergents dissolve cell membranes?
Yes they can dissolve membranes and are even used to isolate active forms of membrane proteins by solubilization. The product are micelles of a lipid-detergent mix and a protein-lipid-detergent complex. Maybe you find this short abstract interesting.


  A critical step in any in vitro analysis of membrane proteins is the
  solubilization of the membrane to extract the protein of interest in
  an active form to obtain an aqueous solution containing the membrane
  protein complexed with detergents and lipids in a form suitable for
  purification and further analysis. This process is particularly
  delicate as the aim is to maximally disrupt the lipid components of
  the membrane while putting the protein components in an un-natural
  detergent environment without perturbing them. Looked at this way, it
  is remarkable that it ever works. Although the process is difficult
  and hard to master, an increasing number of membrane proteins have
  been successfully solubilized in active forms, allowing some general
  principles to be established that we illustrate in the method
  developed in this chapter.


Duquesne K., Sturgis J.N. (2010) Membrane Protein Solubilization. In: Mus-Veteau I. (eds) Heterologous Expression of Membrane Proteins. Methods in Molecular Biology™ (Methods and Protocols), vol 601. Humana Press