I think it might be possible. Try adjusting your sleep time to a larger time window including the hours you napped.
I just slept from 2230 to 0555, within the sleep window I'd set at 2230-0700. Then I managed to have a nap from 0730 to 0830, a much needed decent solid nap which set me up for the day! Before the nap I adjusted the sleep time to 0730-0830. That didn't work. It seems there can only be one sleep time per day on my Garmin app. So then I tried adjusting the sleep time to 2230-0830, and bingo. Turns out I actually had deep sleep during my morning nap. The next time I have an afternoon nap I'll try extending the sleep time to something silly like 2230-1600. I expect it will just do the same, adding sleep time together, and showing 'awake time' for the times I'm awake. Not sure how it will work out for resting times though. It might log them as 'light sleep'. Let's find out.
Result: without being able to edit sleep stages, this won't work well enough.
Last night I was awake from 4am to 5:30am. Oddly, when the phone first uploaded the data, this was reflected correctly in the chart, although an earlier stage of the night when I was asleep was incorrectly identified as awake. A few minutes later it had adjusted to mostly light sleep for both periods, correctly for the earlier one, incorrectly for the later. This is understandable because both periods had about the same amount of movement.
So it thinks I've had 9h10m when I've actually had 7h40m. I wish it were possible to simply edit periods of my sleep time to correct such inevitable errors. This would correct the current problem as well as effectively enabling an accurate nap time recording feature.
Thanks everyone for the factual answer (i.e. not supported).
That said, I agree with SAHO. As a customer, I would expect that "sleep tracking" includes sleep in general - not a narrow definition that requires me to read fine print.
In other words, a product of this price point should actually solve the customer's problem.
I continue to find evidence that my device is overpriced and and under-delivers on feature quality (GPS accuracy is another). I hope that if enough customers with this sentiment speak up, Garmin will do something about it.