I know that the Nexus 4 has Slimport technology, which is very close to MHL but draws little/no power. However, is the Nexus 4 still able to use an MHL to HDMI adapter?
The Specs at GSMArena mention TV-out (via MHL A/V link), which suggests it should work.
On the other hand, ExpertsReview states:
Which suggests the standards are incompatible (other sources I consulted underline this). An even clearer hint you'll find in a review by anandtech:
As this shows, there're SlimPort adapters available which are not that expensive (though not that cheap either), and are probably better fitted for your purpose. As you either yet have to buy the cable, I'd rather go for the right one.
I have not bought yet, but I guess Chromecast might do the trick anyway for more recent devices.