Hi Adrien,
You're certainly 'allowed' to do this. How you treat the resulting information is another question I think. PF2 doesn't implement the models you need here, which are those with an ascertainment bias correction. Because of this, I think a pragmatic route might be to first run PartitionFinder on your data, and to then use the partitioning scheme it suggest, but ignore the models. For the models it would be more appropriate to use those with an ascertainment bias correction.
An alternative is to put the invariant sites back into your analysis, as you mention. That would be my preference, because the ascertainment bias corrections are rough guesses, whereas the invariant sites contain precisely the information that the standard models need.
Rob