Is there any way to see a tree of directories with a chmod of drwx--x--x ? I know I can manually check by bash script with if [ -d dirname ]. However it is not the solution I am looking for.
No. You do not have read permissions on the directory and so you are unable to view the contents. Since you only have execute permissions, all you can do is attempt to use filesystem objects which may or may not exist within the directory.