The stamp does not buffer the serial input so if it were away doing something else at least part of the serial input would be lost. Also the stamp does not have interrupts.
I'm currently working on an RS232 daughterboard for the Parallax MoBoStamp-pe. By using one of the onboard coprocessors to handle the serial I/O for this board, it will be possible to buffer characters in the background while the BASIC Stamp is busy doing something else. However, the BASIC Stamp will still have to poll the coprocessor periodically to see if any characters have been buffered. Release date is likely to be a few months away.
Meanwhile, http://www.rhombus-tek.com/co-processors.html -- their "Simple Multi-Tasking" 8-pin coprocessor has a built-in recieve-only buffered serial port, so that might solve your problem.
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- Stephen
-Phil