'Fraid not, Rob.
No.6-32 is actually 0.138" dia which makes it roughly 3.5mm dia
No.8-32 is 0.164" dia which is roughly 4.15mm dia
The pitch of 32 tpi is also much finer than the std pitch for either m5 or m6 threads
I still say five thirty-two rather than five thirty-seconds.
Mind you, the place where I did my engineering had fairly strong American connections.
I would never say six thirty-two though ... its either No.6-32 or three sixteenths, depending on whether you're talking threads or dimensions.
And finally ...
I have to say, I still prefer working in thou (..sandths of an inch) when I'm machining.
I know that sounds like being a luddite but it isn't really .. its just that its a more appropriately sized unit for the job in hand.
Tenths of a mm are too big and hundredths of a mm are too small.
And both are too much of a mouthful.
There, I've said it now .. I'm sure I've let myself in for criticism.
Oh, and by way of excusing the digression, I will just say once again ...
Gazza's adaptors are fab.
I've been using one for ages and its been perfect.
And welcome along, Sandro.