No. EGR reduces peak combustion chamber temperatures because exhaust is not combustible, so diluting the (combustible) air/fuel mixture with (non-combustible) inert exhaust gas means the fire in the cylinder is not as hot. Go read up on EGR (better, more detailed description in the Stockel and Peterson books described in this thread.)
The EGR doesn't change the air/fuel ratio in the carb....it slightly leans it after the carb
No. The EGR does not affect how rich or lean the mixture reaching the cylinders is. It affects how dense, in a word, the combustible air/fuel mixture is.
When the EGR was not working, the HC's read higher than when it was.
Right. That's not because the mixture goes rich with non-working EGR, it's because there remains some unburned HC in the exhaust, and a portion of that is sent back through the engine (via EGR) and thus burned the second time around, leaving less unburnt HC at the tailpipe.