NO, they cannot conduct electricity.
Because they have no Free mobile electron. We all know that in solid electrons are carrier of electricity while ions are carrier in liquids.but note that some non-metal can conduct electricity like graphite an allotrope of carbon.
Firstly, there are non metals that can conduct electricity (ionic compounds), except they have to be dissolved to do that. One example is the salt used for cooking (NaCl in chemical formula). When dissolved, the ions are able to move freely and conduct electricity. Otherwise, like other non-metals, the particles are held in the structure and able to move freely, resulting in non-metals being unable to conduct electricity. Although metals are also held in a structure, they have free moving ions that can conduct electricity throughout the metal, allowing it to conduct electricity.