Yes, it certainly is possible, and it's commonly done on
factory guitars like many Ibanez and those Fender "Fat"
Strats & Teles, and the Lone Star strat for example. On
your project guitar, it would depend on whether the
polarity of the single coil pickup was opposite the
polarity of the humbucker's one coil of the pair you
chose to connect together in combination. If the magnet
polarities are opposite, then you can experiment to find
which of the two coils in the HB will hum-cancel in
combination with the regular single coil. It is possible to
get hum cancellation but have the coils wired out of
phase, producing a weak nasal sounding signal. So for a
normal signal, you would prefer to have both coils
in-phase but opposite polarity.
 
It really comes down to experimenting with coil
combinations using the particular pickups. The best
way to get through it is to use some short alligator test
clip leads to connect any pickup leads to the output
jack. Make notes of wiring for each connection. When
you come up with the magic combinations you want, go
back and figure the selector switch wiring. Do the
soldering of the delicate leads last, after all the stuff is
worked out. Your resultant wiring will look much
neater, like you actually planned it, rather than it
looking like an experiment. You know what I mean.
 
When paralleling a full humbucker with a single coil
there is a partial hum cancelling, because only half the
HB will be in opposition to the SC. There's a large net
winding "single coil" hanging in the air and picking up
stray fields. In the situation where you have tapped the
HB so that only one coil is in combination with the
other regular SC pickup, so that hum is minimized, you
still may not get full cancellation because the turns
count on a HB's coil bobbin is typically lower that the
turns count on a Fender-style single coil pickup. That
difference in turns count is going to pick up stray fields.
The smaller the net imbalance, the smaller the hum
signal received.