Hello Steve and welcome to the forum.
CBT-I techniques are effective for people with chronic insomnia who take sleeping pills and they are effective for people with chronic insomnia who do not take sleeping pills.
To answer your question, yes — eventually you would have fallen asleep without pills. That’s because nobody can stay awake without sleeping at some point. Sleeping is a bit like breathing. Just as we can hold our breath, we can temporarily suspend sleep (usually due to worry about sleep). However, eventually, the body will take over and force us to sleep, just as it will take over and force us to breathe.
If you aren’t sleepy, then you probably aren’t going to sleep. However, it’s important to bear in mind that it is very easy to forget the cues of sleepiness when you have been living with insomnia for a long time and you have very high levels of arousal.
You might find this quick video I recently recorded to be helpful (check out the comments section, too):
https://www.youtube.com/watch?v=UjWdsuOsTt0
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