I strongly suspect the answer is no, but I feel like there should be a question here about this for people to find more detailed information about as these outbreaks become more common.
From what I have read, some strains of E. Coli are heat-resistant, so it's not a good idea to think that cooking it will kill the bacteria if present. Also, you might contaminate your cooking utensils or other surfaces that do not encounter the heat. It's safest to just get rid of it.
The problem with Romaine Lettuce (specifically) is that the vast majority of people eat it raw. That is why the U.S. CDC was so fast to put out an E. Coli alert, Nov 26th telling people to throw away any/all the Romaine you had. The illness was popping up, but the CDC couldn't pinpoint the origin of the tainted lettuce. Their swift alert prevented (possibly) 100's of deaths. Fortunately, E. Coli Prevention is relatively simple (handwashing, cooking thoroughly, avoid cross contamination, etc.). And for now... don't eat the Romaine.