Provided you have got the signal polarity correct, you can get away with doing
this due to the way RS232 is specified.

Although the levels are spec'd to be +/-3V minimum, the spec requires a
threshold at a slightly positive voltage, so that if you have an open circuit
line the pull down resistor which should be terminating the input of the
receiver will keep the receiver in the "marking" state which the negative
voltage would hold it. If you check the data sheets for receiver chips such as
the 1489 chips, you will find they have a schmitt trigger set to about +0.5v to
+1.5V below which the out put will "mark". If this did not happen there would be
continuous interrupts to the CPU from the UART.

Doing this is not without a disadvantage. What you do lose is noise immunity,
which should not affect you just going around the room. The large voltage swings
normally used in RS232 are what give it reasonable noise immunity except in
(electrically) very noisy environments.

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