Avast Business security does not directly log the traffic. It can block certain websites but is not a true web filter.
However as David and Eddy have eluded to, you are giving up certain things using your personal device for business. For example, while avast doesn't log the traffic, your Admin may have an appliance at the gateway logging the web traffic such as a web filter or advanced firewall (SonicWall, Barracuda, or similar)