Is illusion a good enough substitute for Sneak? I plan on making a magic using only character and I want to join the Thieves guild and the dark brotherhood with him. I need to know if the quests for the factions are possible (or at the most, moderately challenging) to complete with only having level 15 sneak and level 100 illusion. I plan on having most to all of the illusion perks. If it is very difficult, or if it's impossible then please let me know.

Your Sneak will level up just from sneaking around enemies, for example in the Thieves Guild, sneaking through houses to steal keys or sneaking past guards, so you'll finish with higher than 15 Sneak.

I have yet to try out Illusion in this game, but I've seen videos on YT and it seems pretty promising.

Due to the "Advanced" detection mechanics, you have to "sneak" in order to avoid being detected. But, at least you don't have to invest perks into sneaking.

Join the DB and get the muffle enchanted boots. Combine that with Invisibility and detection shouldn't be a problem, at least if they can't see you. I was standing up running in circles behind a bandit and he couldn't detect me until I took off my boots and he somehow discovered me that instant. This was with a very low sneak level and no invisibility.

Ok, I didn't think about that, let's say I have level 65 sneak with no perks. If I have 100 illusion with all perks, is that a reliable substitute for having no sneak perks?

With muffle shoes and invisiblity hell yes. Unless you physically touch someone they wont see you. But if you cast invisibility while someone sees you, they will still detect you for a certain time depending on how good your sneak is. But on my illusion character I can sneak, cast invisibility, then stand up and SPRINT in a town and no one detects me. Muffle is very important for this.

OK, that's perfect, thanks for the information everyone.