Does subwoofer + bookshelve=full range speaker?

It can almost do it, provided that you can cross your sub in as well as the designer of your speakers. With full cognizance of all the parameters involved. This is unlikely. But, is a possiblity. The other problem is, that subs, in fact, are directional, and the location out of the line-source will make a difference, and turn your system into an "array" instead of line-source. Typically, this affects imaging, in this case in the bass region. This is not to say that you couldn't get an acceptable result, and many people are happy with the results they get.

"if you add a subwoofer( assuming a good one) to B&W 805 or Martin logan entry level model . do you get the same performace as N801 or prodigy or more because the subwoofer in many instance will go even deeper than the full range speaker?"

NO

"if not why not?"

The 801 has a different xover (maybe even using better parts) and it uses a different midrange driver (the surroundless ones whereas the 805's have a surround made of rubber). The Prodigy should also do more in the top-end and midrange than the smaller logans. The same tweeter in two different systems can sound different too. Depeding on the sub you choose you may get more bass extension than the bigger model of the same manufacturer, but it turns into apples v. oranges at best. There's also the phase issues.

If your question supercedes B&W and ML, then I can tell you I am using Reference 3A MM de Capos with a SVSubwoofer- total retail $3200. I have owned Genesis Vs ($12K), Accoustat 2+2 and 3+3s, Chateau References (monitors) with dual Sunfire MK II subs ($6K+). The de Capos SV Sub combo is by far the best I have had. I will add a second sub for stereo. My room is 19X 31X 14.

If you are interested in trying this combo, my de Capos are for sale (see ad/auction). I am a dealer and getting their new "i" version.

While the above points about sub integration are valid, they fail to mention one of the biggest advantages of the sub/sat approach: the ability to site the sub to optimally deal with standing wave problems, and to site the sats to image optimally. No full-range speaker can do this as well unless you happen to be incredibly lucky. I would add that the only subs I would consider are the RELs, which are designed to cross over extremely low and come in under the natural rolloff of the sats. I am not a dealer or otherwise affiliated with REL, but in my experience all other subs have problems integrating seamlessly with the sats, probably mostly because they cross over much higher and/or put the sat signal through a crossover. Until REL came along, I would have said that sub/sat systems were hopelessly flawed, but not anymore. Lastly, try to find a reasonably sized full-range speaker with flat extension to 10Hz. On balance, I would say that properly done, a sub/sat system will significantly outperform a full-range system of equal cost.

"the same performance"?

From the perspective of soundstaging and image control, you may well get BETTER performance. I would have to pay a LOT more to get what I currently have with my Nautilus 805s and my REL Stadium III Sub. I personally do not find the 805s to be all that light in the 30-50 Hz range (partly because of the amp I use) I would like to lose the metal dome tweeter, however.

If your goal is to reproduce the cross-over designs of the 3-way, I would expect the answer to be no.

If your question has to do with whether or not you would like what you HEAR with monitors or planars plus sub, the answer might be yes.

In my price range, I have to live with trade-offs, and this is one that personally pleases me.