The main issue connected with using approximate components such as approximate multipliers in deep convolutional neural networks (CNN) during the design process is the necessity to emulate them due to the lack of native support for approximate operations in modern CPUs and GPUs, which is computationally expensive. To accelerate the emulation of approximate operations of CNNs on GPUs, we propose TFApprox4IL, a software library supporting both symmetric as well as asymmetric quantization modes, approximate 8xN bit multipliers emulated using lookup tables, a new type of approximate layer known as approximate depthwise convolution, and quantization-aware training. The TFApprox4IL performance is extensively evaluated in the simulation of approximate implementations of MobileNetV2 and ResNet networks on Nvidia Pascal and Tesla GPU architectures. Furthermore, TFApprox4IL is also evaluated in neural architecture search (NAS) algorithms to automatically design CNN architectures that directly employ approximate multipliers. On two different NAS methods, EvoApproxNAS and Google Model Search (GMS), we show how approximate multipliers can effectively be incorporated into the CNN design process. To estimate the energy consumption of the approximate CNNs, AxMultAT tool based on Timeloop and Accelergy is introduced. Contrasted to the highly optimized GPU-based CNN simulation implemented using exact arithmetic operations available within TensorFlow, the average overhead of the inference and training, introduced by TFApprox4IL, is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$13.6\times $ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$8.0\times $ </tex-math></inline-formula> , respectively, considering ResNet50V2 and MobileNetV2 CNNs on ImageNet and CIFAR-10 data sets. This overhead was reduced by one order of magnitude with respect to previous methods.