No. You will not be able to add or access alts in Final Draft Writer.
If you would like to use this feature, you will need to open your file in the desktop version of Final Draft 13.
For further information on utilizing Alts in Final Draft 13 you can visit this link:
How do I add alternate dialogue?
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/