I have to agree with the others here, don't try the method you are thinking about, been there done that, and for all the reasons JM mentions it just plain sucks!
Why take the time and effort to pick a good router, and then stick it in a substandard table?
If you need, really NEED to just get one thing done in a router table (I've been there too) just cut a hole and mount the router in a 3' x 2' piece of plywood, even half inch will do, get a really straight 2x4 or an off cut of 3/4" plywood and clamp it to the "table". Support the table between two saw horses, or in a workmate like fixture. I've done this on site, and it works, well actually, for basic routing.
I would not spend the time and effort doing what you are talking about, but that is just me, I'd rather spend the time and do it right, once.
My granddad always used to say
Why is there enough time to do it right the second time? Why not just do it right the first time and be done with it?
Also as someone mentioned, you have to seal both sides of they plywood base, if you put the hardboard on one side, it will warp in time, as the hardboard seals that side of the plywood, the un-hardboard side will absorb moisture faster, and this will warp the plywood.
Good luck, I'm not trying to be negative or discouraging, but trying to save you time by sharing my experiences, as in I've done what you are thinking about doing, and while it does work, it does barely work, and like they said, it gets old quick.