It would depend on which view you're playing back.
If you're in session view (with columns for each track) then you're correct, the clips are only storing the "dry" signal or midi notes, and being passed through the Instrument/VST chain when played.
However, if you record your sound (with VST processing) onto the arrangement view, (with rows for each track) it will be recorded after the processing chain, meaning the track on the arrangement view will be the "wet" signal, with all processing included.
Note that, because of this, changing the VST configs will not change what's recorded on the arrangement view. However, by clicking the gray "play" button at the very right end of the arrangement view timeline, that will transfer control of that track back to the session view, so you can dub over or re-record it.
It's also quite easy to record onto the arrangement view, just click the record button at the top and start playing stuff in the session view. You may need to click the orange play/pause button to take control back from the arrangement view first, depending on if you've already played tracks on the arrangement view.