If I enter the keywords "Topic Name" into the search form, can Low Search also find entries that have been tagged with "Topic Name"? This would be something similar to Solspace's Super Search "keyword_search_category_name" parameter.
Yes. From the docs:
Low Search v2.4+ can also add category information to the index, making entries searchable by keywords present in their categories. Just like the regular channel fields, you can add weight to the category name, description and any of the category custom fields.
Note: if you’re using ExpressionEngine 2.7+, making changes to a category will automatically update the index for the associated entries. However, if you’re using an older version of EE, you will need to rebuild the index manually whenever you edit or delete a category.