Q: Can I boot Mocha CFW with Haxchi?
A: Yes, but use it only if you need redNAND.
Why? Is there a reason you shouldn't use Mocha on sysNAND?
Maybe I can rewrite the question and answer to make it less confusing.
If you want a Custom Firmware on sysNAND, you don't need Mocha because CBHC or Haxchi can do it, and way faster !
You can do this : CBHC or Haxchi -> Patched SysNAND
instead of this : CBHC or Haxchi -> Mocha -> Patched SysNAND
So, yes, you can use Mocha from CBHC or Haxchi if you only want sysNAND; but you'll get unnecessary load time as mocha is longer to patch the system than CBHC or Haxchi.
If you want redNAND, then Mocha is the way to go. but if you want sysNAND you can use both CBHC/haxchi or Mocha, but why wait more for the same* result?
* Almost the same !
There is a reason you'd want Mocha on sysNAND : WUP server.
CBHC doesn't add WUP Server/client feature. that's one of the reason why it's faster to patch sysNAND. But you don't need or use WUP Server every day. run Mocha only when you need it.
Edit:
The answer was 1 question below:
Q: Why should I launch Mocha only for redNAND?
A: If you want only a CFW to launch or install games, it's a LOT faster to only patch sysNAND.
I still added precision to the question, it's now like this:
Q: Can I boot Mocha CFW with Haxchi?
A: Yes, but use it only if you need redNAND. Booting into a Custom firmware SysNAND using Mocha is unnecessarily longer while Haxchi can do it faster, unless you need WUP Server.