It's bad. I was put on sleeping pills by my therapist. But I love to exercise in the morning!
Today was my first experience with this problem. I thought the pills' effect would have vanished by morning but no. Plus, I like to exercise on an empty stomach very early in the morning. So today was like my worst day of exercise ever.
I didn't realize it in the beginning but halfway through my workout I had this weird and unusual feeling then realized that I was still sleepy/drowsy. I had to stop.
Whatever the case I don't think eating would prevent me from feeling the effects of the drug.
What can I do? Changing to the evening is definitely a no-no because of my schedule.

Talk to your therapist. Maybe they can given you a different medication with shorter effects or change the dosage.

Also, maybe with consistent exercise they will decide you can wean off the sleeping pills?

I'm all fine now. The antidepressant is even kind of reducing my appetite. So yeah, it was a matter of time, just to let my body adapt to the new treatment.