As another way to think about it, why not use BitLooker to exclude those folders from the backup, then in the properties of the replication job specify backup files rather than production storage as the source?
In case you wanted your replication to occur evey X minutes that approach would require you to backup your VM every X minutes, which is not very convenient I believe.
but does the replication job currently skip files such as the memory dumps, paging, and hibernation files (if they exist)?
Yes, there is an option to exclude swap file blocks and deleted file blocks in "Advanced Settings". Please see this
article for more info.