Scan Guy,
As such the fouling due to deposits wil occur at the low points of the slug catcher only, to be precise at the produced water outlet end which by design as you know is the lowest point. As far as fouling in other sections d/s is concerned ideally it would not foul except if the gas being wet and corrosive is leading to corrosion products like Iron sulfide scale and other muck. In this case you may have a fouling scenario in equipments like a gas gas exchanger, condensate reboilers, produced water degasser etc.
Citing our own experience i can tell you that if you have been using foam pigs for pigging the disintegrated foam pieces would definitely end up in your dowmstream exchangers.
Hope this info helps