If the relatives you are trying to verify have tested DNA, then yes -- you would get matches to relatives at the 2nd and 3rd cousin level. Enough of those matches should help you verify the great-great grandparents. When you get your results you should also check out www.gedmatch.com -- you can create an account there with the dna test data from here and perhaps locate others who are relatives who have tested at FTDNA or 23&Me.

FTDNA will also let you do a free upload and will show you the top 20 matches without paying for an account there.

Patience is needed in this hobby.