Short answer is yes. This will require some knowledge of the HTTP Protocol and how the target web site is organized.
Connect to the target web site with TCP/IP. Use HTTP POST and HTTP GET methods to send and fetch from the site.
The HTTP Client Vis may provide enough functionality to do what you want. If not, you can form the queries with the TCP/IP primitives and strings. Refer to the World Wide Web Consortium Web site atwww.w3.org for more information about HTTP method definitions. There are some examples on the NI web site.