In this paper, we investigate the feasibility of learning GNN (Graph Neural Network) based solvers and GNN-based heuristics for specified QBF (Quantified Boolean Formula) problems. We design and evaluate several GNN architectures for 2QBF formulae, and conjecture that GNN has limitations in learning 2QBF solvers. Then we show how to learn a heuristic CEGAR 2QBF solver. We further explore generalizing GNN-based heuristics to larger unseen instances, and uncover some interesting challenges. In summary, this paper provides a comprehensive surveying view of applying GNN-embeddings to specified QBF solvers, and aims to offer guidance in applying ML to more complicated symbolic reasoning problems.