Inversion of tracer test data
You sure can. Inversions of tracer data (or any other breakthrough curves), however, have their own challenges, specifically if you have a pulse injection. Weighting is an issue (but iTOUGH2 supports many options), as well as the presence of numerical dispersion. Nevertheless, you can study all this using iTOUGH2, which supports data types such as >> MASS FRACTIONS or >> CONCENTRATIONS etc.
Most likely you will not estimate saturation directly (which is generally a state variable (i.e., an output of TOUGH2), not a property (i.e., an input to TOUGH2). Instead, you estimate other hydrological parameters that yield a saturation distribution that is consistent with your tracer data. (An exception is if you want to estimate initial gas saturation).