Asterisk instead of modem connections in client/server app

Has anyone had an experience of implementing a dial-up real-time synchronous (not voice) interface between a client application and a server using Asterisk? We have an application that uses modems for establishing connections and we would like to get rid of the modems. Asterisk looks promising but I am not sure if it can do the job.
The setup I was thinking about was Client->PSTN->PCI Card->Asterisk->SIP Client->Server app. Any input will be highly appreciated.