This thread has been really productive, so I hate to throw out the bag of flaming poo....
But I just want you guys to be aware of recording phase related audio signals [example Snare Drum, and Overheads] through two separate brands of AD conversion.
The Latency of one converter brand might be [for sure] different from another brand, so...this Latency between converters can drastically change the phase relationship of your microphones, should you decide to use the Kick Drum Mike through the Digi AD, and one of the Overhead Mikes through the Added Converter Chassis. The latency might not even be a sample or two, but thats enough to cause a phase shift, and enough to remove your kick drum from the picture.
Bottom line, you can use different converters for tracking but you must be aware: if you're miking up every bell, whistle, chime and triangle, they had better be going through the same clock and conversion. Overdubbing is NO problem and even recording amp land [through one set of AD's] miles away from drum land [though another set of AD's] its not a problem, why.....Because of BLEED! If there is no bleed, there's no problem. Overdubbing has no issue using separate converters, just make sure you're converters are locked and in sync.