Not according to the way CC permit holder INSTRUCTORS advise their students. Not a single instructor I have spoken with advocates assuming this is true.
Multiple DAs have stated that "that interpretation" (that a CHL allows the carry of an otherwise illegal knife legal) is not what was meant by the legislators when they passed the CHL law. Now some people say that it doesn't matter what they (the legislators) MEANT but how the law READS, which is what you are doing.
This is why we end up needing case law, to "interpret" years after the fact what some legislators may or may not have meant because the wording is unclear, someone disagrees with what the says literally (this case) or some set of LEOs and DAs decide they want to push the issue one way or the other.
Oh, wait - we do NOT have a test case in Texas yet on this interpretation of the CHL law and how the wording actually affects 46.02.
We almost had one a few years ago when someone tried to enter the State Capitol with a 6.2" knife and a CHL. He was arrested by a committee of DPS Troopers who couldn't decide who was right. After a significant amount of time and money was spent on lawyers, the Travis County DAs finally decided that they weren't going to pursue the case and dropped the charges. Probably because they did not want to be the test case and loose and end up setting said case law precedent. Most likely, because every one the DAs office spoke with advised them that they had no chance in hell of getting a conviction.
I know that had I been selected to be on the jury, a not guilty verdict would have been rammed through so fast, the judge would not have had time to undo his/her robes to pee. BUT.....
Do you want to be the test case? Not me.
Just wait until we get the illegal knife laws purged.