I recently came across this question and no it's not originally one of my own however since I saw it I thought that I would awnser it as openly and honestly as possible.
As specially since I myself tend to wear diapers/nappies from time to time as a adult who is in his 40's, I would have to say the awnser is both a yes and no it really depends no pun intended on what cloths you wear on the day.
On the average day I tend to just put my regular clothing on over the diaper and hopefully nobody notices anything
However as I've found out the hard way there's no guaranteed 100% fool-proof way of hiding the fact your wearing them at some point your clothing will give it away when you bend down or if it's showing above your pants.
If anyone asks me any awkward questions about why I wear adult diapers I am quite prepared to say either one of two things
#1. I suffered a horse riding accident in 1996/1997
Or/
#2. that I had epilepsy from 1992/1993
Or/
#3. And if that doesn't work then I say I am disabled and that's usually enough.
Or ultimately go away and mind your own business although that's a last resort.
However personally speaking I would recommend if your wearing a diaper just wear what ever is comfortable over it as you don't want to be too tight or too loose as that's just un-comfortable, also take into account the weather on the day when deciding on what to wear before going out of the house.
I myself tend to wear either trousers or shorts and a t-shirt and a jumper/Fleece if needed depending on the weather on the day in question
and I always take my rucksack as my preferred diaper bag although it's really up to you what you use.
But generally you don't want anything too tight as it will show up everything and be at risk of ripping which is very embarrassing.
But conversely you don't want anything too loose as they could fall down or get snagged on something revealing everything or worse leak which is so humiliating and not to mention embarrassing.
My advice would be to just go with what feels right for the day and have fun don't worry about what other people might think if you have to say anything just be polite and say something like I do.