Can we detect pulsars that aren't "pointed" towards us?
They don't need to be pointed exactly at us, since the angular beam radius is a few degrees (Pulsar Astronomy, P. 212) but there is a portion that we can't detect, described by a beaming factor (P. 211):  

  

The larger beamwidth at higher energies can be seen in these graphs:


R. N. Manchester 

We mostly can't see "ordinary neutron stars". "neutron stars can only be easily detected in certain instances, such as if they are a pulsar or part of a binary system" - Wikipedia

If the pulsar is radiating gamma rays more isotropically (but still varying with phase as in the Manchester charts), then these could be detected.