Thank you for posting your question on History Hub!
Unfortunately We cannot give a definite answer on that as it mostly depends on the time period of the land grant application and how thorough the application was filled out. Normally yes, they contain some information on the applicant, and sometimes they can reveal where the applicant lived. We would suggest you research this and see what turns up as there is not much information for us to go on here (such as the name of the applicant, dates, etc.).
For researching land grant applications, you can search the website of the General Land Office, Bureau of Land Management. It’s user friendly, easy to navigate, and a great place to start.
We also suggest that you review the NARA Land Records website and the finding aid titled Research in the Land Entry Files of the General Land Office (Record Group 49) for more information.
We hope this information is helpful and best of luck with your research!
You did not give any indication of the time period you were interested in for NC land grants. This website give a lot of information about NC land patents and grants (especially colonial ones) North Carolina Land and Property • FamilySearch