I just press Shift+P, hit Enter and I have a plane, not sure what you're talking about.
In your context, 'plane' = 'patch'. 'patch' is the terminology used by DR, so that's how mission authors (and all the documentation) refer to it.
'Pressing Shift+P, hit Enter' gives you a patch that matches the size of the last object selected in the editor, as viewed in the currently active Orthoview. If a brush was selected, the default is to remove the brush (which might not be what you want, in which case you need to uncheck the 'remove brush' box). If a model was selected, the default is to simply give you the patch.
You then size your new patch to the opening you want to place the visportal in, texture the patch's face with the Vis Portal texture, and now you have a patch which at first glance might appear to provide you with the visportaling function you desire.
1 - A patch has no depth, so it's a line in the orthoview when viewed from the side.
2 - A patch has no back face, so the camera view won't show it when viewed from the back.
3 - (And most importantly) dmap ignores it, so the visportal doesn't work.
You're better off creating a brush the size of the visportal you want (sealing the edge faces to worldspawn), and pressing 'Brush->Make Visportal'.