I'm not familiar with that test. However, cervical cancer and the precancerous cells (dysplasia) that precede it is very detectible with PAP smears and biopsies done if / when you have an abnormal PAP and colposcopy. Cervical cancer is rare and takes many years to develop from precancerous cells. So if you get PAP smears per recommended guidelines (every 3 years for most women) then any abnormalities should be easily found (and treated if necessary) before any cancer develops.
I cannot speak for this nagalase test for other types of cancer.