Hi,
Yes, this will work, at the point that the server host both websites, the host domain will remain in the HTTP header all the time, also when the LB sends the connection to the server.
So if you collect a capture on the user PC and on the server itself, you will see that the domain name will remain the same, this is assuming that there are no redirects.
So the application must be able to differentiate each request.
Hope this answer your question.
Rodrigo