There are quite a few factors.
It should appear in both HW2.0 renders and also MentalRay renders. my IBL image always shows up both in viewport and renders.
However when saving/exporting images with Alpha channels, the background is masked out by the alpha channel so if you don't interpret the alpha channel it will disappear.
If you are using After Effects for your footage then render PNG sequences and then in AE do this:
Import the file sequence (or still) as per usual. Then in the PROJECT window right click on the sequence.: INTERPRET FOOTAGE>MAIN and tick 'ignore alpha'
If you save your Maya files out as a format which doesn't support Alpha such as Alpha then it should show up. Be mindful of the Gamma settings.
Notice in Maya you may get 'pinched' pole vectors (funny join in the sky/floor apex) in the interpretation of the square-to-sphere. this is pretty hard to avoid but its possible to instead place your 360 map the texture on a sphere with 'best effort to outsmart the pinch UVs' (I've included an MB file attached for you to see, you just need to put your 360 image in the colour node of the sphere's material).
Still this is not perfect in terms of pole pinch but then I would be tempted to re-capture the 360 as a skybox (cubemap) and then you can fix the top/bottom sections more easily in photoshop. In my experience cubemaps are the only satisfactory solution to this.
I use this rig to re-capture scenes as skybox panels
https://www.creativecrash.com/maya/script/cubemap-skybox-6-camera-setup
Console yourself that mapping/projecting spheres out of rectangular images is a problem far older than CG, it's been a problem for a few hundred years to cartographers 😉