Keep in mind there are 2 variables called $request_time, one in ngx_http_core_module and another in ngx_http_log_module.
Without having looked at the code or tested it, I believe that these variables only represent elapsed time from when the first byte from the client request is read by NGINX, and stops when the request has been processed, or been processed+logged.
While I don't interpret these as including the "network round-trip time" (e.g. client in California, server in NY, RTT = ~80 msec), it may take some time for the entire blob to come in off the wire and into the NIC, be fully read by NGINX (or the kernel if sendfile is being used), and then be processed by the server application (which could be busy doing something else).
The speed of the network can definitely affect the result if the request is large, or the network is slow, or the connection suffers from loss or congestion causing TCP to re-transmit or slow down - which could be further exacerbated by the RTT.
All things being equal, the way I read it, the value is not a direct measure of the RTT, but it can be affected by crappy network conditions, the TCP stack overreacting to said conditions, as well as the application response time.
--
SuperTCP for NGINX
www.supertcp.com