Hello,
Yes, you can simulate tsunamis with Telemac, just by giving the information of elevation at a boundary, and using the Thompson boundary condition. However in some cases (large amplitude or long distances) tsunamis are not a solution of shallow water equations and you must use either Boussinesq equations (which are also solved by Telemac-2D) or even non hydrostatic Navier-Stokes equations (Telemac-3D). There is a paragraph on the solitary wave and comparisons between equations in my book "hydrodynamics of free surface flows", and it can be checked with the tests cases given on this site.
With best regards,
Jean-Michel Hervouet