Not usually. Gundam uses MINUIT to minimize the negative log-likelihood (NLL) function and find the best-fit parameters. For this process to work reliably, the NLL surface must be smooth, well-behaved, and contain a clear global minimum. Attributes related to the model, parameterization or input uncertainties/correlations can create a likelihood surface that is difficult to optimize. Thus, non-convergence is often a diagnostic signal that the model or inputs need refinement, rather than a failure of Gundam.
Gundam features multiple spline interpolation methods, and they have different approaches for when the spline extends beyond the boundaries. A not-a-knot spline performs cubic extrapolation by continuing the cubic polynomial defined by the first/last two points of the dataset. This maintains agreement with splines generated using ROOT's TSpline3 class. A Catmull-Rom spline extrapolates linearly beyond the defined knots.