In general it is accepted in HCI research  that the presence of progress indicators enhances the UX of an interface by providing a degree of interactivity, responsiveness, and informativeness to its user. However, it has also been demonstrated that the style or implementation of a progress indicator can have an important impact on the user's enjoyment and perception of an interface .
As for your specific question regarding the piecemeal loading of web pages, I believe there are several factors that come into play. If a web page has several components that take a long time to load (or the user is on a less-than ideal connection, i.e., through a smartphone), piecemeal or on-demand loading of page components can have a profound effect on the user's perception of the responsiveness of the interface. On the other hand, I have seen studies that show that heavy use of progress indicators can actually give users the perception that delays are longer than they actually are (this finding was driven by the desire to find out how long to wait before displaying a progress indicator when doing an asynchronous operation, however, so its findings may not be generalizable to this situation).
I could not find any research evaluating this specific technique, however, the software industry seems to be adopting it as a valid approach to designing "heavy" pages. Whether or not such techniques require progress indicators (as in your Facebook app example) remains to be seen but likely depends on the efficiency with which remote content can be received.
: Brad A. Myers. 1985. The importance of percent-done progress indicators for computer-human interfaces. In Proceedings of the SIGCHI Conference on Human Factors in Computing Systems (CHI '85). ACM, New York, NY, USA, 11-17. DOI=10.1145/317456.317459 http://doi.acm.org/10.1145/317456.317459
: Sumaru Niida, Satoshi Uemura, Hajime Nakamura, and Etsuko Harada. 2011. Field study of a waiting-time filler delivery system. In Proceedings of the 13th International Conference on Human Computer Interaction with Mobile Devices and Services (MobileHCI '11). ACM, New York, NY, USA, 177-180. DOI=10.1145/2037373.2037401 http://doi.acm.org/10.1145/2037373.2037401