Not necessarily. The computer doesn't throw a code if anything is wrong, it throws a code when it sees a specific output from a part. The stuff is pretty 'dumb' in that regard. There specific triggers for specific parts. And even at that, the trigger may not always be accurate. A code for XYZ may not mean the part is bad. Likewise no code doesn't auto-magically mean good. Unfortunately, this type of stuff is why you need 2 way scan tools to any detailed diagnostics anywhere, and why diag services can be so expensive. Admittedly, it's kind of where the parts cannon meme came from; replacing stuff that makes sense at first glance, but is really just shot gunning parts at the issue with crossed fingers
It's like... Imagine you're making toast. But you burn the toast. At which point do you say the toast is overdone, vs the toast is inedible? The computer only says its inedible, but you might be in the overdone range and it'll say nothing.
My point being.... The 4l60e is electronically controlled. The computer takes its shift queues from things like engine temp, engine load(MAF, MAP, TPS), engine RPM, current gear, speed, etc. If something is happening to present bad info to the computer, it won't make the appropriate decision in regard to shifting.
I'm not saying your trans is good - the transmission in these trucks is more suited to a v6 in a car rather than a v8 in a 3 ton barn. They're pushed to the limit and fail accordingly. BUT, just because it's a common issue doesn't mean you should just condemn the transmission over any little hiccup. Do some digging, save yourself some cash.