If their chakra is drained and replaced by orochimaru, I'm just a little confused as to how that doesn't disrupt their chakra.
Clearly their chakra does indeed become overwhelmed.
Why?
The cursemark drains their chakra to the point where it can be easily overwhelmed by the chakra being pumped into them.
Proof?
As was already said not only in this thread but also Kakashi told Sasuke in the chuunin exams that if he used his chakra, his curse mark would instantly overwhelm him. As soon as he used chakra, the seal would begin sucking up or believe it or not sealing his chakra into the SEAL. And sasuke, being unable to control it would lose all his chakra and die.