If adapters are identified in your sequencing reads, they should be removed. Why would you consider leaving them in? I'm curious. Is your library preparation kit the Illumina Nextera?
Personally, I do scan and trim adapter "since it is not a bottleneck in the analysis" rather than leave it for the aligner. also, I prefer using Fastp over FastQC for inspecting the quality of reads and then performing any necessary corrective actions. Fastp can handle both tasks in one go, and you can also control its behavior. Below is the basic command for Fastp: