To answer your question they way you have written it, the answer is "No" you cannot make a plane parallel to your view (or line of site).
The only way to make a plane is by using either some geometry or by using the existing Planes (Front, Right, & Top).
I'll bet you have some geometry already available for you to use, if not that's fine too. You can use the geometry (like MadMango and myself have already mentioned) to control your plane whether it be by using 3 points to make one plane. Then taking that plane you just made and creating another one from that, which is at a 45 degree angle,(you have to pick a line or an edge of the geometry for it to work). Then you take that one, an offest another new plane etc. etc. etc. You may have multiple planes in there but you will get there sometime.
Or
If you have more geometry that needs to be made in the file. Go ahead and build that Geometry. You may find that this leads you to the answer you seek. Then again, you may need to re-think your approach to the model your building.
If you do not have any Geometry to work with, then start making some sketches to work with. Use these sketches to offset planes and what ever other means you need to get to your parallel view.
It may take multiple planes and sketches and possibly features to get there.
I had to make a plane like your talking about a long time ago, back when I first started using SW95-96. I didn't have the convenience of NG's to ask my questions. I had to find them through VAR's and my own knowledge (No training ever). It took some time to find it, but it stuck with me to the day. I figured it out on my own without any help. (other than busting my head on the monitor a few times):-D. When I was finished I had 4 planes I didn't need, other than the fact they were parents to the plane that I needed to make the sketch then the feature.
So my answer to you is play with the planes a bit, see what you can come with. When you give up on it, let me take a stab at it. I love good challenges. ;-)
I hope this helps, Scott Baugh, CSWP

George Koch Sons,LLC
Evansville, IN 47714
sjb@kochllc.com