I have an archer with similar skillset on Master. I only use Alchemy, no Enchanting at all and it's perfectly playable.
Hmm, this is encouraging. I'm playing on whatever difficulty it defaults to...adept or something? So that's good to know. Do you get hit enough to make light armor perks work it? In my head, with high stealth and the illusion magic as a backup, I shouldn't be taking too many hits unless I do something really stupid. My first character is nowhere near done, but in Oblivion I liked to keep a second character with a totally different feel on backup if I just wanted an occasional change of pace (and my hypothetical build should do just that).
No skill is required for play in this game... in fact, the three characers that I've played have all ended their careers before level 42. There's no "must do" or "must have" to comment on in this game.
I realize.

I'm OK to run with sub-optimal characters -- my current, first playthrough is an orc mage, and orcs of course aren't exactly prime spellslinger candidates. What I DON'T want is a totally unplayable character. I got my fill of those in Neverwinter Nights.

Edited for typos.