Can nexus one phone or any similar android phone work, when its microSD is pulled out from it, and if only internal memory remained.
Yeah definitely it works fine without any issue. But if you have installed any apps on SD Card then they won't work at all. But to take backup of any data(Contacts, Messages, Call log) on your phone you should have SD card inserted.
Finally to answer your question, yes. it works fine as the OS and related information stored on the phone internal memory.