If the script file is
will fail because its the wrong name.
If you ensure that there are no 'x' perms set, then even ./appserver.sh will fail, BUT if its valid bash code, then 'bash ./appserver.sh' will run and you can't stop it even if there are no 'x' perms.
It would help if you explained why you want to do this.
You can certainly make it root owner/grp accessible only, in which case only root can run it (which is what happens with the service cmd..)