When you have a system in balance where the gas pressure from the regulator, lines, and head space of the existing kegs is at the same pressure, and that pressure is in equilibrium with the existing beer itself, and you add a non-carbonated keg, the not carbonated keg will naturally create a lower pressure atmosphere and will draw co2 away from the gas lines, which will in turn draw co2 from the head space of the existing kegs and from the regulator. However it'll only be 15 seconds or so before the regulator has got the whole system back into a sort of equilibrium again and so this shouldn't affect the carbonation levels of your current kegs in any meaningful way.
However, once the new keg starts absorbing co2 into solution it will again be very slowly drawing co2 out of the gas lines which will in turn be coming from your other kegs and from your reg. The reg will then balance the pressure as well.
So you shouldn't have any carbonation issues with your existing keg.
BUT the transfer of co2 from keg headspace to keg headspace can naturally move beer aromas as well which may not be desirable. I haven't ever noticeably had this problem but it does exist in theory.