Separating Lipids from Milk
Milk is mostly water, and diluting it (roughly speaking) with sulfuric acid to a concentration of ~50% milk and 50% sulfuric acid will result in a very acidic, but still aqueous, solution.  We can examine the likely behavior of other milk components using basic chemical principles.


Sugars.  Milk is rich a variety of di- and oligo-saccharides such as the eponymous lactose, as well as many other more complex molecules:  


  [Free oligosaccharides are natural constituents of all placental mammals' milk. Human milk contains 7–12 g/L oligosaccharides, making the oligosaccharide fraction a major component of human milk. Compared with human milk, the concentration of oligosaccharides in the milk of the most relevant domestic mammals is smaller by a factor of 10 to 100.]


Fortunately, the effect of sulfuric acid on the sugars is easy to predict: they will simply stay dissolved in aqueous solution.  Hydrolysis of the sugars is possible, but will not happen to any great degree without heating or prolonged incubation.
Proteins.  Milk contains thousands of unique proteins.  However, by far the most predominant proteins are called caseins.  Caseins are relatively hydrophobic, proline-rich molecules and in milk are present as tiny aggregates -- a colloid -- of molecules.  Adding sulfuric acid will denature the casein.  As a result, the casein molecules are likely to stick to each other and form a centrifugable pellet that goes to the bottom of a centrifuge tube after spinning.  Proteins contain amino acids linked via amide bonds that are unlikely to hydrolyze in the acid, unless very high temperatures or very long incubation times are used.
Phospholipids.  Phospholipids in milk include glycerophospholipids and sphingolipids.  Polar lipids play an important role in stabilizing the triglyceride (fat) emulsions that keep fat in solution.  They do this by forming bilayers and other structures on the surface of triglyceride microdroplets.  To do this job, phospholipids have a phosphate head group attached to a fatty acid tail.  The fatty part of the phospholipid sticks to the triglyceride, and the polar head group interacts with aqueous solution.  The polarity of the head group is tunable by pH.  At neutral to mildly acidic pH, the phosphate head groups are (negatively) charged, greatly strengthening their propensity to interact with water and maintain emulsion stability.  

Phospholipids may be partially hydrolyzed by the acid, but without very high temperatures or prolonged incubation, most molecules will remain intact.

The strong acid conditions that arise from adding $\ce{H2SO4}$ will protonate these head groups, neutralizing the negative charge and vastly weakening their emulsifying properties. 
Triglycerides.  Triglycerides are the molecules that provide most of the fat content of milk.  They are triacylglycerols.  Unlike phospholipids, they have no polar head groups, and thus they do not dissolve in water.  They would "want" to form a separate, oily phase from the water (just like mixing vegetable oil and water), but the fact that they are usually bound in tiny droplets by phospholipids prevents this separation.  Because triglyceride oils are less dense than water, if they did ever get the chance to coalesce into large droplets, they would rise to the top of the milk.  This happens when cream naturally separates from fresh (raw) milk, but in homogenized milk, the droplets are artificially forced to much smaller sizes, effectively preventing the droplets from coalescing or rising.

Upond acidification, the loss of phospolipid surfactant activity breaks down the stability of the fatty droplets, allowing them to rapidly coalesce, so they rise to the top of the tube, a process that is only accelerated by centrifugation.

Hydrolysis of triglycerides in the acid is possible, but unlikely.  In addition to required prolonged incubation or high temperatures, keep in mind that the separated triglyceride phase is actually not exposed to the acidic solution very much at all.