Yes, knowing they are under an Iowa (or Wisconsin) test will change their behavior---and most likely create all sorts of biases in the results.
And you're probably right; time constraints will most likely place subjects into system1 thinking.
Subjects' having knowledge about an experiment may generally ruin it, for it can make testability collapse (how will others reproduce the results?). There are, moreover, all sorts of confounding factors that may directly influence subjects' behavior. Also, one cannot argue that 'they were concentrated on the task at hand', as they knew what was expected. One of the basis of empiricism is to not intervene (as in the Milgram Authority experiment, for instance). In most experiments, subjects will either hear a fairytale story of what they are being asked to do, or are simply told no background story. For example, experiments on priming with money generally hide the goals from subjects (See also Bargh and colleagues experiments on priming, which follow the same route, and were considered extremely controversial by psychologists until the last years).
Of course, this is not a straightjacket rule. One can do psychological experiments in which the subjects know what they must do and they should only "respond truthfully". Perhaps the most famous example of those was Ariely's "adult" experiment (It's quite a read). I have also conducted experiments in which subjects knew the goals completely, but one (control) group could not achieve it (low-skill group versus high-skill group, such as chess grandmasters). Ideally, however, subjects should be blind to the actual objective of the test conducted.