Will a lower resolution while rending cut down rendering time
Rendering in lower resolution will


Downscale the video, which takes very little additional processing time
Take less per frame time for the video encoder to compress


You should definately notice a significant gain in rendering speed if you switch from 1080p to 720p, and I cannot imagine what the other person meant, by "will always result in longer rendering times".

Of course if you cancel a rendering process which is 95% through, just to change the resolution, you will not have gained much, since the renderer has to start all over again.

Also there might be some video software on the market which is so incredebly bad that the situation I described above is reversed. But this shouldn't be the case, especially if you render with video codecs like h264, which always need a lot of processing time.