You should be ok , just searching for a name on facebook , however you may not be able to access that persons information , but you will see his/her friends .
If you have a friend / mutual friend that that has this person as a friend , then this persons name will pop up as a person you could add as a friend , ( suggested friends )
however , that person will not know that you did a search of their name .
Only that next time they log-in , they may see your profile , as a suggested friend .