Edge computing offers the distinct advantage of harnessing compute capabilities on resources located at the edge of the network to run workloads of relatively weak user devices. This is achieved by offloading computationally intensive workloads, such as deep learning from user devices to the edge. Using the edge reduces the overall communication latency of applications as workloads can be processed closer to where data is generated on user devices rather than sending them to geographically distant clouds. Specialised hardware accelerators, such as Graphics Processing Units (GPUs) available in the cloud-edge network can enhance the performance of computationally intensive workloads that are offloaded from devices on to the edge. The underlying approach required to facilitate this is virtualization of GPUs. This paper therefore sets out to investigate the potential of GPU accelerator virtualization to improve the performance of deep learning workloads in a cloud-edge environment. The AVEC accelerator virtualization framework is proposed that incurs minimum overheads and requires no source-code modification of the workload. AVEC intercepts local calls to a GPU on a device and forwards them to an edge resource seamlessly. The feasibility of AVEC is demonstrated on a real-world application, namely OpenPose using the Caffe deep learning library. It is observed that on a lab-based experimental test-bed AVEC delivers up to 7.48x speedup despite communication overheads incurred due to data transfers.