From my understanding, there's two methodologies for flex fuel, sensor based and inferred. I believe ECMs typically support one or the other, so there's not much of a choice there.
edit: found info that suggests the '08 LE5 (Cobalt Sport, formerly SS/NA) is actually an E37
E16A (early L61): can't be tuned
P12 (LSJ): no flex fuel support
E37 (late L61/LAP, '08 LE5): can be pinned for a flex fuel sensor
E67 ('06-07 LE5): can be pinned for a flex fuel sensor
E69 (LNF): inferred (kinda?)
As much as I'm not an expert in any sense here, I know significantly less about anything that's not a P12, so take all this with a grain of salt. I don't believe any Cobalt came set up for flex fuel, but the E37 and E67 ECMs can have a flex fuel sensor pinned in. I believe the E69 with its built in wideband can compensate for fuel composition changes, but it's not a true inferred flex fuel setup, meaning you're in for a bad time thinking you can go from a spot-on 93 tune to a full tank of E85. You might be ok with a solid E47 tune when the E85 pump is actually E70 on a bad day, but that's all speculation.
To answer the original question that was asked, I believe the early L61s had different crank and/or camshaft position sensors, so the E16A ECM can't be easily swapped for the E37 ECM (which can be flex fuel tuned). I'm not sure if an aftermarket ECU or an engine + factory ECM swap would be easier.