We investigate whether GPT-2 acquires Swedish grammatical structures in the same implicational order as for human second language (L2) learners, as predicted by Processability Theory (PT). We present SwePT – a minimal pair dataset targeting Swedish syntactic and morphological structures that are acquired by human L2 learners on four separate stages of language development – and evaluate the GPT-2 models on SwePT using an acceptability classification task throughout fine-tuning with different input orders in regards to the grammatical structures identified in the data. We find that the observed acquisition orders correlate across the fine-tuned models, while violating the implicational order sequence as hypothesized by PT. The observed relation between performance on the classification task and frequency distributions of the contrasting features in the minimal pairs suggests that the acquisition order can be explained by unigram and n-gram heuristics. While the adaptation of NLP methodologies into the PT framework requires further conceptual and methodological refinement, we do not find evidence for PT-like grammatical development in our experiments.