Yes it does, shifts still have to be paid for. A death curse simply gives you a free tag on all of your consequences and allows you to inflict multiple (instead of the one you normally get) consequences on yourself at once if you have the space. "...all of the consequences he has can be tagged, and he can inflict more on himself..."
This. Death Curses are not
unlimited. You must still summon power, but you get some free tags from your consequences. You don't need to control it, because you're assumed to take the entire amount as backlash. To get an idea of scale for a Death Curse, an example:
The Wizard in question dies to an enemy who walks up to him and thrusts a (non-Warden) blade through his heart. No time to cast defensive spells, but time for a Curse. He had taken no consequences previously, and has Lore 5, a +1 complexity bonus appropriate to the curse he's decided on. He has three Fate, and at least three aspects appropriate to the casting. So, the complexity would appear to be:
5 (Lore) + 1 (complexity specialization) + 2+4+6+8 (sacrifice of unused consequences) + 2+2+2+2 (tagging all consequences suffered) + 2+2+2 (invoking three aspects) = 40
So his curse could be anything he could do with 40 shifts of Thaum. No control needed (assume it fails and he takes 40-shifts worth of backlash to no effect more significant than the decapitation). No time take, it's a reaction to the swing of the decapitating blade.
Note that this is not assuming a highly-specialized build. If the character had a Conviction 5 (and therefore another consequence), it would go up. More specializations in Thaum complexity would improve it. More available invocations (or possibly some appropriate free-taggable aspects) would help. On the other hand, if the Wizard had already been wounded previously, it would go down (because he wouldn't be able to sacrifice those consequences, though he'd still get the additional free tag on them).