ECU running in closed loop mode primarily meters the A/F ratio in response to the MAF sensor and Lamda sensor. The larger displacement engine will draw 10% more air per revolution but the MAF will sense that increased flow and the ECU should be able to work out the fuel needed to achieve A/F ratio. When ECU runs in open loop (just using inputs from throttle position and intake pressure, without MAF) then the exact displacement would be critical to get right. My understanding is that open loop is only used by Bosch ME7.5 ECU as a fallback such as when the MAF is unplugged. The larger engine would likely run fine in closed loop with the stock 1.8t ECU, at least well enough to drive and get through the smog test. Possible that the stock ECU might have some difficulties if you tried to run it hard to RPM redline under full boost as the stock injectors might get maxed out?
Smog checks generally just check the concentration of pollutants, not the mass-volume. A 10% larger engine is not necessarily producing different concentrations of pollutants that would be detected by sniffer, just 10% more exhaust overall (at WOT). If smog inspection station checked the block number and figured out it was a 2.0 or notices other hardware changes, then those might fail you.
In order to compensate for the change in displacement and keep open loop operation working too, you would need to adjust in numerical constants in the ECU .bin file related to engine displacement; KUMSRL & KISRM . Search & refer to info in
http://nefariousmotorsports.com/forum/index.php to figure out how to do this. It would likely only take a knowledgeable ECU tuner a couple of minutes to make the needed change and this should not trigger any problems with smog inspection check (such as when emissions related features like SAI or O2 sensors are deleted).
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