You don't say what voltages you have?
Pull the 6V6 and see what heater voltages you have from pin 2 to pin 7 (use clips & connect up with the amp unplugged from the wall). Then, if you have >6.3VAC, reinstall the tube and measure plate, sceeen & cathode voltages.
If the 6V6 is blow then no, you won't have any sound, there's nothing else to transmit sound from the preamp to the OT. Most blown tubes look fine on visual inspection.
I wouldn't leave a 5881 in there for long, plate current will rise as will cathode voltage (usually beyond the 25v cap that most people fit) and the cathode resistor will be stressed. For a quick test to determine wherther the amp works you should be OK.