No, due to the differences between the two metals; how they react when in contact with each other and how they conduct electricity. Aluminum expands differently compared to copper and also causes it to deteriorate due to galvanic corrosion. Eventually this will cause arcing and open connection or even fire.
Aluminum wire connections can overheat and start a fire without drawing enough current to trip the circuit breaker. Combining the two wires is NOT recommended, and connectors like this are extremely specialized and only offered by one or two other manufactures.
Gardner Bender FAQ 