In order to execute, the execute bit must be set. Even the owner of a file cannot ask the system to execute it if it's not marked as executable.
The one caveat here is that in the case of most shell scripts, you can execute them by calling the shell yourself and feeding the script data to it as an argument.
This would execute the
sh shell and send it the text data for your script to be executed. This only requires read-permission on the file because the shell is what is being executed and it only needs to read the script not execute it.
You can change the permissions of files that will be written by setting the umask in your ftp preferences, or use a shell later to
chmod them. Some ftp daemons also support changing the permissions on existing files.