Is it possible for a device to consume more power than it is wall-charging?
Yes, it's definitely possible.  Most USB chargers are fairly limited in their output and devices like tablets are not really designed to be used while charging, unlike laptops.  You'd think it would be OK to simply sit and remain on while charging and unused, but perhaps the Nexus 7 does not have very good power management.  You might want to look at having sync pause while the device's screen is off.

If you want to crunch the numbers and verify what's happening, take a look at my answer here about the PS Vita.  If you get the specs/numbers for the Nexus 7 and its charger you could do a similar analysis to see whether the power use is exceeding the charger's output.