I'd say its possible but unlikely that someone reprogrammed their Speak n Spell. The first tricky thing is the TMS5100 voice synthesis chip uses a complex LPC-10 encoding to encode the sound with a very low bit rate (1100 bits/sec). Basically it's modeling the filter characteristics of the vocal tract. So the first problem is you have to convert your audio signal into this representation, which is going to be really, really hard unless you have access to the TI system that does this conversion.
The second problem is the speech data is stored in a TMS6100 ROM which is kind of a strange chip: the 14-bit address is loaded 4 bits at a time, and then the ROM steps sequentially through memory from there. The point is that you can't reprogram this chip (since it's a ROM), and emulating it with a standard EPROM would be a big pain.
I should point out that I don't have firsthand experience with these chips (apart from using a Speak n Spell years ago). But I happen to have been studying them in detail a couple weeks ago for random reasons.
For more information on this chipset, the datasheets are at http://www.datasheet-pdf.com/datasheet-html/T/M/S/TMS5100_Te... and http://www.ti99.com/exelvision/website/telechargement/tms610...
I just did a search and found someone who hacked new words into a Speak n Spell a couple years ago. But he needed to use a CPLD (like a FPGA) to simulate the ROM, and a Windows LPC encoding program, so this wouldn't have been possible in the 80s. http://furrtek.free.fr/index.php?a=speakandspell&ss=1&i=2