Well, simply put, the the channels are locked on a per-console basis, rather than a per-sd basis.
So, if you manage to install a channel on your Wii, it should copy to and from that Wii just fine regardless of SD.
The only time you will have problems is, as tueidj has stated, if your sysmenu IOS happens to be a version that has the fakesign bug fixed, and you try to copy over a wad with a fakesigned TMD.
Speaking of fakesigned TMD, the main reasons that they would be modified (and consequently fakesigned) is:
1. Because they may be a hacked version
2. An "injected" VC title
3. Homebrew wad
4. Had their region flag changed (such as "regionfreeing it") since channels have their region flag in their TMD
Or possibly:
5. The person who made the wad was lazy and used a packer app the signs both the ticket and TMD by default, rather than just the ticket.