The upcoming sixth generation (6G) of wireless communication systems is expected to enable a wide range of new applications in vehicular communication. However, the use of multicarrierbased modulation in vehicular communication introduces challenges due to the Doppler effects, which can induce nonlinear distortions at high-power amplifiers (HPAs) and significantly degrade channel estimation. In this paper, we investigate the performance of long short-term memory (LSTM)-based channel estimation considering the nonlinear HPA memory effects. Our results reveal the impact of these nonlinearities on the detection of transmitted signals, highlighting the importance of considering these often neglected effects when developing vehicular communication solutions for practical scenarios. We further present a lowcomplexity method for compensating for part of the NLD memory effects on the transmitter side, while handling the remaining distortions along with channel estimation. In addition, we emphasize the ability of certain estimators to handle these distortions at the receiver and present their advantages for tracking the vehicular channel.