Data can only produce noise with his mouth, and we've only ever seen him produce one sound with his voice at a time. So he would be perfectly singing the Doom melody, but only the lead part

Data: "Geordie, It appears you have accidentally downloaded 'Duke Nukem' to my neural network!"

'It is time to kick ass and chew bubble gum, and I am all out of gum!'

'Guess again, freakshow. Duke is coming back to town, and the last thing that is going to go through your mind before you die ... is my size 13 boot!'

I think you would be seeing if you could get data's hair to run doom.