hello and welcome to the forum,
yes, by default rclone does that.
https://rclone.org/docs/#use-server-modtime
"Some object-store backends (e.g, Swift, S3) do not preserve file modification times (modtime). On these backends, rclone stores the original modtime as additional metadata on the object."
dir file.txt
08/14/2021 07:18 PM 273 file.txt
rclone copy file.txt remote:test -v
INFO : file.txt: Copied (new)
rclone lsf --format=pt remote:test -v
file.txt;2021-08-14 19:18:56
