No. You will not be able to use Production features like Revision Mode or locking pages in Final Draft Writer.
If you would like to use these features, you will need to open your file in the desktop version of Final Draft 13.
For further information on utilizing production features in Final Draft 13 you can visit these links:
If you need to install your copy of Final Draft 13, you can do so here:
https://www.finaldraft.com/support/manuals-and-software/fd13/