The short answer usually...yes even though the question itself isn't as black and white as you're making it. If you take a mp and compare that to the literature mp for that substrate it's safe to say you're typically in the upper 90's for purity when it comes to the amine you're talking about(generally).
However, the long answer is no when it comes to other substrates where you have isomers with similar mp's. An analytical chemist who is a friend of mine would agree that purity is a combined, multifaceted approach to quantifying a substrate. 1H-NMR and GC-MS are often the standards of measuring the 99% grade mark but like a said a simple melting point test is a pretty good starting point.