At least as far as the Schwinn le tour models go, the serial numbers weren't on the bottom bracket shell until 1984; my 1983 has the serial number on the dropout, but the '84 has it on bb shell.

As far as '80's Schwinns having serial numbers that are reliable, I'm not sure many of them do, at least not the Greenville ones. The Greenville-built Schwinns often have serial numbers starting with "S" (which might indicate Greenville), then a letter representing month of manufacture, then a number representing year of manufacture. Such as the serial number starting with SG4 I mentioned above, which would seem to indicate Greenville, July, 1984. But we've discussed a bunch of these Greenville-built Schwinns here, and there are inconsistencies.