Yes, the existence BCC will destabilize BCT mining.
Everyone knows that at equilibrium, if BCC has 1/10th the value of BTC, that the hash power mining BCC will be 1/10th that mining BTC.
What is less obvious what happens when the system is not in equilibrium. Imagine that the market reprices BCC 100% higher and BTC 10% lower. What is the expected distribution of hash power now assuming short-term profit-maximizing miners?
The answer is "most of it will be mining BCC." Because the difficulty adjusts only very slowly (every 2016 blocks) BCC becomes twice as profitable to mine as BTC. Hash-per-hash miners would earn double by mining BCC. This continues until the difficulty reset comes when BCC would go "limit up" (4X), when most miners would leave BCC back for BTC. BCC's difficulty would slowly ratchet back down due to its fast difficulty adjustment and the process would later repeat.
What this suggest is that at times when BCC is more profitable to mine and the hash rate migrates to BCC, the average block time for BTC will increase significantly and BTC's already slow and expensive transactions will become much more so.
Umm..what?
How is 25 BCC (at 10% the value of BTC) mined per day more profitable than 300 BTC per day?
So, you are incapable of imagining: "Imagine that the market reprices BCC 100% higher and BTC 10% lower. What is the expected distribution of hash power now assuming short-term profit-maximizing miners?"