I can tell you, however, that the PC will receive data from the
    PIC without one. Just remember you need to send the data
    inverted, which means you can do it with a bit-banged interface
    but not with the PIC's internal UART.

A long time ago, after observing that the SDK-86 requiring +5 and +/-12
used the +/-12V ONLY for the rs232 drivers, I connected the +12 supply to
+5, and the -12V to GND, and it worked fine (talking to a CPM system,
IIRC. (yes, that long ago))

Since then, I've had a very "liberal" view of rs232 requirements. :-)

There have been a couple of ciruits published (here?) that do clever things
when at least one side has "real" rs232 voltages and "typical" rs232 signal
leads.  Ie, rather than switch between +/-PWR, you can go between +5 and
"whatever is on DTR (which is supposed to be -V, and I can damn well MAKE
it be -V since I control the PC side software too.)"  (This is slightly
more clever, IMHO, than using the modem signal leads to create a "power
supply" for a traditional level converter circuit.)

BillW

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