I love my Pentair IntellipH. It works well with, and requires, an Icxx IntelliChlor. They're not cheap, though. It's a good size. It shuts down the IC when it is injecting, so you don't have chlorine and acid mixing together (bad!).
How bad is it if both inject/run at the same time? They are both very "metered" small doses. As long as the pump is running, would they be diluted enough to not cause a problem, even running at the same time?
If it is bad, what are the consequences? Are we talking about the general (but important) don't mix chemicals, especially acid and chlorine, that we all should know about? Or is it other side effects or problems that can occur when they are mixed in such diluted amounts?