No — using the Local Search Rank Checker, you do not need to include a geo-modifier to get localized rankings.
What is a Location / geo-modifier?
An example of using a location / geo-modifier in a keyword is:
'plumber in Chicago', where 'Chicago' is the geo-modifier.
The reason for including a geo-modifier is to localize the search results down to a specific area, as opposed to simply searching for 'plumbers' across the whole country.
With Local Search Rank Checker, you don't need to do this, as you'll set a search location for your report.
Setting a Search Location in your report
1) In Local Search Rank Checker, click the 'Actions' dropdown, then 'Edit Report'.
2) In the 'Search Settings' section, enter your search location in 'Set your Search Location (Google & Bing only)'.
3) Click 'Verify Location' to finish the process.
This Search Location is then set on the search engine to ensure that the search results are localized.