Are you using a proper mic and setup?
In order of my preference
1:
Record it properly like a studio recording (vox separate to backing), then record a sync video afterwards.
You can, of course, sing in the sync video, cos you're not recording the sound from it.
You just have to be sure to do it with exactly the same timing as the recorded take.
2:
Record it properly like a studio recording, but use a little earbud for monitoring, and film it at the same time.
If you don't mind proper headphones in the video, use them instead.
Bounce the audio, having done a sneaky mix, and line it up with the video in some other software.
3:
If you just want a live room recording then yes, you could play the backing out through the laptop or a hifi and record the heap.
Just be aware, it'll sound exactly like a guy doing karaoke in his room.