Can I use a sheet of plywood to get a tighter hardwood floor?
You can do it the way it was suggested, starting with the ripped plywood, yes, will need a spline to change the direction of the floor to fill in the space that was occupied by the plywood, and you will still need to face nail the last 3 or 4 pieces, since the floor nailer will not fit that tightly to the wall. You will need to rack out the flooring and compress it in place using a lever system to draw it all up tight, before it is nailed tight, again, only with the last 3 or 4 rows. The lever can be a prybar with a block of wood to keep from breaking into the drywall or a tapered 2X something to act as a lever

OR

You can do it the way I seen it always done, and the way I do it myself when laying floor in a room with a simple floor plan.
Some guys don't take the time to mark the floor joists, they figure I guess many nails will hold and I am sure it will. If you mark the joists first at the starting edge. Then chalk a line 3/4" wider than your flooring is onto the subfloor, lining the first row of flooring tongue of the T&amp;G flooring on the chalkline. This should give about a 1/2" space to the drywall or framing, which is required, if you use the tongue of the as the reference. This will get covered by the base and shoe mold. To keep this space though not needed in my opinion, you can set 1/2" thick plywood shims to maintain the space.

Now back at nailing. It is a simple operation once the joists are marked, usually on the wall so the base will cover it or use blue painters tape if perhaps the base is in place. That way when you put the paper down you still have reference marks. Next take your longest, straightest strips and set them on the chalk line as mentioned before, set them on the line and shoot 2 nails at each joist location, 1/2" to 3/4" in from each edge of the flooring. Do not worry how the ends of the flooring happen at the joist. You can add a 3rd nail in the tongue, like the flooring nailer that you will eventually use will do. Move on to the next row. This will be nailed once on the face and once in the tongue and do the same for the 3rd row. That should get you to where your nail gun can take over.

Just a mention on the laying of the floor. Maybe you have instructions, maybe you don't. I want to impart some techniques on laying a high quality floor. Just 3 or 4 tips.


Keep the ends of your flooring apart from the next row by at least
6", more the better, but if it needs to be closer than that, so be it.
When possible, do not let the breaks (ends) in the flooring line up on subsequent rows no closer than the 3rd row out.
Use as much of you can of that short stuff in a closet or pantry if you have one. 
This one regards layout, check the room for parallel
            walls, tweak it here or there if you need to so a difference will
            not show up on the other side of the room, then it is too late to
            fix. If 2 people are nailing the floor, have them switch sides
            periodically, one person always drives the floor tighter than the
            other. When you get halfway across, measure the room again, you may
            be surprised how the dimension changes. With using more force or
            less on the hammer, you can actually "steer" the floor to finish
            well on the other side, granted, if the difference isn't too drastic.

Good luck