Glad you asked. Of course wet soggy paper is not a viable option, but air filters rarely get very wet unless riding in a monsoon which Alex might experience sometimes.
I usually fit the air inlet velocity stack that comes with the carbs I am using. For example on a CB77 I use CB750 carbs and they have a nice long and well designed stack. On our 240cc CB160 race motor I used VM28s and found some stacks that work well.
On the dyno we tested with short and long stacks and wih no stacks and the difference was less than 1/2 a HP with the slightest tilit in the curve as expected. I prefer to smooth the air flow into the carb and on a GT750, we ran the CV carbs with UNI filters, stock air inlets and with special ultra short Lectron type stubby inlets and no discernable difference in rideability power or reversion.
Our TZ motors always run open. No stacks no filters, just open and the reversion can be seen at low revs with fuel stand off behind the carbs.
That's why I suggested that he run it on the dyno so he can see what that motor likes with those carbs. I would expect stacks to be best, followed by good large volume filters and then open carbs a little way behind. I am a big fan of well designed velocity stacks and IIRC when David Vizard tested them decades ago, a stack with slight taper and rounded intake flowed about 5% more than open and some flowed less than stock. Straight tube lost 6.7%, straight taper without a flare lost 5.5% and the best was Lectron style which added 5.8%. In that testing he found/proved that all that really matters is a radius on the intake end. Without a smooth intake, flow is disrupted.
On our old motors where we need every tiny poofteenth of power, that stuff matters. On a 1300cc behemoth i doubt that any of us here would notice the difference in power but driveability could be impacted.
That's why I suggest that if he buys it, he should find out for himself. he's a smart man and not afraid to try things that the rest of us are sure won't work. Sometimes they do and sometimes they don't.