Coupling recharge with 1D groundwater flow model
If you are not interested in the vertical flow occurring in your aquifer (which I assume is the case) then one can indeed add the recharge to the existing head!

In groundwater issues, we often assume the recharge to be constant over time and equal over distances when considering such problems. This is mainly due to simplification as we are often interested in horizontal flow rather than vertical flow. 

That being said, in general I would consider recharge (as this seems to happen outside the system we are interested in) as a constant rather than a boundary condition.

However, when going into details, considering boundary conditions there are several ways to go:

Dirichlet boundary conditions: Where we assume a constant head at a certain location. As we go from A to B, we could assume constant heads at these location(s), depending on your setup.

Neumann boundary conditions: Where we assume a constant input/output discharge at a certain location. This could also be your recharge but also dependent on your setup.

Cauchy boundary conditions: complex combination of the two where the input is related to a head. An example of this could be a river with head h_x feeding an adjacent confined aquifer with head h_x2

I hope this gives some insight in the application of appropriate boundary conditions. As you can see: it all depends on the characteristics of the system, the known values and your own considerations.    

For further reading one might consider Fitts' Groundwater Science (fully available at ScienceDirect)