Can I take pictures through my telescope with my phone?

The short answer: Yes, but prepare to be underwhelmed. My question to you then would be: Why? If the answer to that is you just want something to text or post to show what you were looking at, go for it, but you're really not going to impress anyone. I have people at public events always wanting to take a picture of the Moon through the scope, and I usually oblige them by taking the picture for them, but it slows the line down and won't impress anyone but total non-astronomy folks (maybe). Still, I get it. People want something besides a memory to take home. Frankly, I'm happy with the memories.

Confession: Against all logic, I sometimes try to take pictures through my telescopes with a cell phone at the eyepiece, knowing it is probably a waste of time. The only decent pictures I've ever gotten were of the Moon, which are still far below almost any image I can find on the internet and the detail I can see visually, and some pretty cool images of Spica and Arcturus with an apodizing mask on my 10-inch. Otherwise, the images suck. Granted, I am using a Pixel 6a, which isn't exactly cutting edge now, so if you have a newer phone, or the latest and greatest (for now) iPhone, then you might have better luck. 

Anyway, here is a gallery of images I took through my 10-inch and 6-inch Dobsonians with the Pixel 6a, as a baseline for what you might expect to get, depending on your phone's camera. I will say it is difficult to get the phone's camera lens lined up with the eyepiece while still being able to snap an image before the object drifts out of view. Although I have no experience with eyepiece phone adapters, the general consensus appears to be that they are fiddly and mostly a waste of time and money. If you do get one, the Celestron NexYZ is often recommended. The images I've seen from them, however, are no better than my handheld images. Phones seem to be much better at getting non-optically magnified images like the Milky Way, or a lunar eclipse over some scenery using their night vision mode, or whatever they call it. Bright comets can be kind of nice.

Left: The Moon rising over the hills. This was so cool that I wanted to take a picture to put in my log for that unique sight, just to remember it better. To me, this is the best kind of use case for taking an image through the eyepiece. 10-inch dob.

Left: The gibbous Moon, zoomed in and cropped to show the level of detail, which is nowhere near what I could see visually. 6-inch tabletop dob.

Left: Spica with the apodizing mask. Pretty psychedelic, but rather pointless. Well, there actually are a lot of points. 10-inch dob. Apodizing masks are used on larger telescopes to negate some of the effects of poor seeing for splitting double stars and seeing more planetary detail. I didn't notice any improvement on my scope, as expected, although the kaleidoscope effect is interesting.

Left: Arcturus with the apodizing mask. Far out, man! 10-inch dob.

Left: Comet C/2023 A3 (Tsuchinshan-ATLAS) through a 6x30 finder. The shot through the eyepiece was too awful even to post here as a bad example.

Left: The same comet using the phone's "night vision" capability, without magnification. Especially with distinctive scenery, this can bring back the memory of the night much better than an eyepiece shot can.

So there you have it. Casual photos? Maybe. Anything more, get a SeeStar or go down the imaging rabbit hole and be prepared to spend some money and a lot of time learning processing. If you want to do planets and the Moon, a basic planetary camera might work for you, but you have to seriously ask yourself why you are wanting to do imaging. It's not for everyone but some people just love it, and it's more forgiving of light pollution.

Astro imaging is indeed a different hobby entirely from visual observing. I remember photographing Comet Hyakutake on a homemade barn door mount with a poorly functioning stepper motor and a film SLR camera. I don't even know where the picture is now, but it was so much less inspiring than the actual view of seeing the comet from that dark sky, stretching overhead like a flashlight beam. 

After that, I decided not to waste good observing opportunities trying to capture something mediocre to take home with me, unless I spend less than a couple minutes doing so out of the apparently primal urge for a tangible keepsake of everything to post on social media.

For me, give me visual every time. I'll find the pretty pictures on the internet—and I do, for placing in my log or notes to go along with my visual descriptions, or just to see what an object can look like to an imaging chip with a lot of computer manipulation.