The assignment task does not provide an IAT procedure, as defined in literature. There is, for example, no blocking if the respondent gave a wrong answer. I am not aware of validated methods to computer IAT D-scores from such data.
Of course, you may perform the formulas as known from Greenwald et al. for the IAT to your data. This, however, is something for your data analysis and nothing that SoSci Survey would do automatically. The automated analyses and D-score computation is only possible within the IAT question type.