Most MCBs have two ratings, one is the once-only break (Icu), the other is the break and survive to serve another day rating (Ics). If you exceed the once only rating chances are it will explode, not a good situation.
However, when you have more than once OCPD in cascade you sometimes get a higher rating depending on the break time constants and I2t limiting behaviour of them. If you take the common case in the UK of a BS88 fuse up-stream of a typical domestic DB then the fuse has this sort of a current-limiting characteristic:
View attachment 99098
If you look along the bottom X-axis for around 16kA RMS PFC and then go up to the plot for a 100A fuse you see it limits the peak current to around 10kA, then if you follow that back to the unlimited line and down you see that is equivalent to the peak of a symmetric fault of around 4.5kA RMS, so your 6kA MCB ought to survive OK.
Also remember it takes very little resistance to bring the current down, 16kA implies Zs is around 0.014 ohm, 6kA would be 0.038 ohm so 0.024 ohms more, with 2.5mm T&E at 19.5 mOhm/m for R1+R2 it is about 1.2m of cable.