Yes, it is possible to have both an ICD and a vagal nerve stimulator (VNS). Having one does not rule out the other. However, both devices produce electrical signals and there is a potential for interaction between them, so careful assessment by both your cardiologist and your neurologist is needed before either is implanted or adjusted.
In practice, the devices can generally be managed together safely with appropriate programming. Your clinical team will coordinate the settings to minimise any risk of interference. If you already have a VNS and are being considered for an ICD, or vice versa, ensure both specialist teams are aware of each other and communicating.