How close to the wind that you can sail with a
spinnaker very much depends on the design of the
spinnaker, both Symmetrical or Asymmetrical. Racers will often have flat cut chutes that can be carried with the apparent wind quite far forward of abeam. Typical downwind chutes are cut much fuller and while they can be carried with the wind forward of the beam, they are generally less efficient than a genoa in those conditions, especially if there is any wind at all. Cruising assymetrical chutes are generally very full cut and really do pretty poorly once the apparent wind approaches a beam reach even though they appear to be usable at closer angles.
Jeff