Yes, there will be cross-talk, especially if the unused channel is left floating (not connected). This will be reduced to a level you probably won't be able to detect if you ground the unused channels. The cross-talk in the ADC IC itself is quite low, so this is bleeding over between channels somewhere on the PCB or wiring prior to the ADC.
When you have multiple microphones and notice cross-talk between channels is too much, then you may need to use a preamp on each mic channel to lower the source impedance, and use shielded wiring from the preamp to Bela. The effect of cross-talk is probably less than what the microphones naturally pick up if located in the same space, so this one is more difficult to characterize. Not sure how you're using them, but supposing you're processing directional information where phase and relative amplitude are important, then on-board cross-talk could introduce too much error into the measurements and you would want to minimize it.