Time-course Model-Based Network Meta-Analysis (MBNMA) has been proposed as a framework to combine treatment comparisons from a network of randomised controlled trials reporting outcomes at multiple time-points. This can explain heterogeneity/inconsistency that arises by pooling studies with different follow-up times and allow inclusion of studies from earlier in drug development. The aim of this study is to explore using simulation: (i) how MBNMA model parameters are affected by the quantity/location of observed time-points across studies/comparisons, (ii) how reliably an appropriate MBNMA model can be identified, (iii) the robustness of model estimates and predictions under different dataset characteristics. Our results indicate that model parameters for a given treatment comparison are estimated with low mean bias even when no direct evidence was available, provided there was sufficient indirect evidence to estimate the time-course. A staged model selection strategy that selects time-course function, then heterogeneity, then covariance structure, identified the true model most reliably and efficiently. Predictions and parameter estimates from selected models had low mean bias even in the presence of high heterogeneity/correlation between time-points. However, failure to properly account for heterogeneity/correlation could lead to high error in precision of the estimates. Time-course MBNMA provides a statistically robust framework for synthesising direct and indirect evidence to estimate relative effects and predicted mean responses whilst accounting for time-course and incorporating correlation and heterogeneity. This supports the use of MBNMA in evidence synthesis, particularly when additional studies are available with follow-up times that would otherwise prohibit their inclusion by conventional meta-analysis.