Yes, System Modeler comes with a small selection of ODE integration methods. To change method, go to the Settings tab of the Experiment Browser in Simulation Center. Near the top of that tab you find the Solver popup menu, where DASSL is the default choice for most models. For many models, the results obtained with the other variable-step method CVODES are at least as good.
There are also three fixed-step methods, all of which are explicit. I must admit that I am not familiar with the inverse Euler method (even though the name isn't that different from the well-known implicit Euler), and I'm afraid it isn't one of the offers.
