Short answer: yes, with no restrictions at all. Telegram Desktop is the official desktop app, and it works with your account the same way every other Telegram app does — as one more session connected to the same account.
How Telegram Desktop sees your account
Telegram Desktop doesn’t “know” or check which mobile app you’re using — official Telegram, Nagram, Cherrygram, or any other client. As far as the server is concerned, every app connected to an account is equal: they all see the same chats, the same unread messages, and any action in one app is reflected instantly in the others.
So “unofficial client on your phone + Telegram Desktop on your computer” is a completely standard setup, no different from “official Telegram on your phone + Telegram Desktop on your computer.”
Is there a feature gap between desktop and a mod client?
Yes, but it doesn’t affect compatibility. A specific mod client’s extended features — say, deeper interface customization or specific chat settings — only work inside that mod client itself and don’t show up in Telegram Desktop. That’s expected: features like this are usually implemented at the interface level of a specific app, rather than stored as part of the account itself.
Messages, media, and privacy settings, on the other hand, stay the same across every device, since they’re stored on the server rather than inside any one app.
What to keep in mind
The one thing worth knowing about is secret chats. Just like when switching between mobile clients, secret chats created on your phone won’t open in Telegram Desktop — that’s a property of end-to-end encryption, not a limitation of any particular mod client. More on this in How to Move Your Chats When Switching to a Telegram Mod.
It’s also worth making sure the account has two-step verification enabled — especially if you regularly log in from several devices and apps at once rather than just one phone.
The bottom line
Telegram Desktop is compatible with any unofficial Telegram client on Android without any restrictions, because both apps work with the same cloud account. The one exception is secret chats, which are inherently tied to the specific device and app they were created on and don’t sync between desktop and a mobile client.