Effects of Filter Topology on transfer function
No - the transfer function of a filter does not depend on the selected topology. However, this applies to IDEAL conditions only. That means: Ideal properties of the active elements as well as for all passive parts (no tolerances).

If these requirements of ideality are not "sufficiently" fulfilled ("sufficiently" means: with acceptable error) different topologies will exhibit different deviations from the desired transfer function. This is the most important criterion for selecting one of the various topologies for a certain application. As an example, the well-known Sallen-Key topology is less sensitive to the opamps finite open-loop gain values (frequency dependent gain) but pretty sensitive to parts tolerances. In this respect, the so called multi-feedback topology (MFB) has opposite properties. 

To select a suitable topology for a specific application is a rather challenging task for an engineer bacause he has to take into account technical as well as economical aspects.  

In short: Under ideal conditions all topologies give the same filter behaviour - however, because nothing is ideal, it is important to select the "proper" method for realizing the filter. In particular, this applies to higher-order filters because, in these cases, we have to select between two principles: Series connection of active second-order stages or active realzation of passive RLC structures (Keywords: Leap frog, active L-simulation, FDNR technique).   

EDIT/UPDATE: For better explaining the influence of non-ideal opamp data on filter performance I like to mention the output resistance of the opamp. Normally, this parameter is always neglected during calaculation (set to zero). However, the Sallen-Key lowpass structure has one severe drawback: For rising frequencies there is a "direct" path between input and opamp output via the feedback capacitor. As a result the damping properties far above the cut-off frequency are heavily disturbed. This is due to a voltage drop across the finite output resistance of the opamp caused by the current that directly goes to the output node.