Hi,
I am not sure if you are asking if you can connect your i-Mix using SIP over POTS, which is not possible. The FXS cards you mentioned normally sit in SIP servers that convert between the POTS and the SIP IP worlds.
If you want to connect your iMix over IP, whether using SIP or Tieline's own session data protocols, the remote Tielines will need to connect over IP as well.
When connecting over IP for broadcasting we normally recommend using dedicated DSL lines so that you are not sharing bandwidth with other devices and can reliably perform broadcasts without interference - this also allows you to use a public static IP address, making it simple to dial from any remote site over IP to the studio. The other advantage is that you can use wired and wireless connections, increasing flexibility of broadcasting from the field.
If you require any further information please let us know.
best regards,
Glenn