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:
The micro USB port also doubles up as a display output, though surprisingly it doesn't use the MHL standard that we've seen on numerous recent devices, such as the Samsung Galaxy S3. Instead it supports the new SlimPort standard, which is based upon DisplayPort.
Which suggests the standards are incompatible (other sources I consulted underline this). An even clearer hint you'll find in a review by anandtech:
When I wrote that review it wasn't immediately clear what advantages SlimPort offered over MHL, which has become relatively ubiquitous in the year or so since its introduction. Since then I've acquired the SlimPort microUSB to HDMI 1.4 SP1002 and VGA (D-SUB) SP2002 adapters from Analogix for testing out SlimPort on the Nexus 4.
As of this writing, the Analogix SP1002 adapter is available on Amazon for around $30 USD. I haven't seen the SP2002 available online anywhere yet, however.
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.