yes it will work as I mentioned just making any search request, it does require some search param ( I used foo in my example) but it doesn't require authentication an dit will kick off th eprocess of completely re-indexing the site. The process can take some time especially for a large site. It is possible to monitor progress to some degree under Administration > Advanced Tools > Task Queue
It will take a minute or so for the task to begin and it will first create index items for each indexable content and serializes them into the mp_IndexingQueue table, than a process on a background thread works its way through those rows writing to the file based index. You will see files appear as soon as it starts processing rows but the files will change a lot until it finishes and then optimizes the files.
If unprocessed rows already exist in the mp_IndexingQueue table it will not rebuild the index because it will think it is already in progress so your steps of your task should probably be
1. Truncate the mp_IndexingQueue table
2. Delete all files from the index folder
3. Make the web request for any random search as indicated previously to trigger re-indexing
Hope that helps,
Joe