Yes, necessarily.
Oil is oil even if it's in conditioner. What, did you think that it changed in any way? If so, how?
Consider this: Have you've ever put oil on your skin and walked out into the sun. I have. Do you know how painful it is? I do. Why do you think it would be any different? What makes you say that it makes the conditioning agents work better?
I ask these questions because last I checked, oil is a
heat conductor.
You're oversimplifying it.
If the practice in question was something like flat ironing, hot combing, or curling the hair with an iron (direct heat), then yes...you are correct. Putting oil on the hair is not advisable, but there are many who do it with success.
For what we're talking about though (indirect heat), applying oil to the hair is just fine. In fact, it's good. The hair doesn't end up fried at all, rather, the cuticles of the hair open up to allow the oil to penetrate and nourish the hair more deeply. This is why you have ladies deep conditioning with pure coconut oil, and adding oils to conditioning treatment.
Also, your analogy is faulty. Yes, oil is a heat conductor, but hair and skin does not respond in the same way to oil and indirect heat. While it may burn the skin on your body, it definitely won't burn hair or even your scalp.
And even that point is weird to me, because tbh, I've never gone in the sun with oil on my skin and been in pain. And when I was a kid, my mom would slather me in cocoa butter and send me out to play looking a piece of fried chicken. Nothing ever happened to me. I've never heard anyone complain about that either. So maybe the sun was just really hot that day in your neck of the woods, because that's the only instance in which I can imagine that happening.
Aaannndd.....all of this is moot, because baggying isn't done with heat at all.