They can, <2008 Berlingo’s did it.
Although if it’s damp enough to notice, you would also notice the coolant level dropping in the engine.
Plenty of other causes, the drains in the scuttle/windscreen being blocked would be #1.
My Berlingo was soaking wet on the drivers side (it would accumulate at least a gallon before the water level got above the carpet). I think because there was a rubber lip seal around the top of the door, it wasn’t the actual door seal but I think it probably kept the wind from blowing rain in against it under pressure and forcing it past. Never managed to get it to seal properly so if it hadn’t been scrapped I’d probably have just drilled a drain hole under the carpet 😂 It wasn’t the heater and wasn’t the scuttle drains so I gave up and just cut the carpet / foam out of the footwell so I could remove it and dry on warm days, it was a shitbox so i didn’t care.