Your question title and question elaboration are not the same.
In general, immunities/resistances cannot be switched on/off. Unlike spell resistance, which is specifically mentioned to have such a switch.
The Dread Necromancer's Negative Energy Resistance grants a bonus to saving throws, not actual resistance in the general sense. Now, characters can always choose to fail a saving throw. In this case, the Dread Necro doesn't want to resist her own Charnel Touch, not that it offers a save anyway. ;)
Wow, because this got derailed into nit-pickery on saving throws (and, correctly enough, there is nothing to cite about voluntarily failing any saving throw, although it is fairly obvious, just like there is nothing to cite about a character choosing to be Helpless against a sword attack 'coz she wants to commit Suicide-by-Town-Guard), I'll try to scope it back to point by focusing on saving throws and how they relate to the situation detailed in the question.
Voluntarily Giving up a Saving Throw: A creature can voluntarily
forego a saving throw and willingly accept a spell’s result. Even a
character with a special resistance to magic (for example, an elf’s
resistance to sleep effects) can suppress this quality. (PH, 177)
This means that even a non-undead Dread Necromancer 9+ can always elect to be affected by negative-energy effects, even though she's resistant to it, whether by the Negative Energy Resistance ability or some other source. Why? Maybe she's got rider abilities contingent on a negative-energy effect. In any case, it's her choice.
Now, take note that the citation also mentions "special resistance to magic" and the Elf's "resistance to sleep effects".
Elf Racial Traits: Immunity to magic sleep effects, and a +2 racial
saving throw bonus against enchantment spells or effects. (PH, 16)
The Elf's "resistance to sleep effects" is actually an immunity, so we can infer that resistances and immunities are essentially the same when it comes to voluntarily accepting magical effects.
Undead Type: Immunity to all mind-affecting effects (charms, compulsions,
phantasms, patterns, and morale effects). (MM, 317)
Because it is worded just like the Elf's immunity to sleep effects, it should be safe to say that an Undead creature can choose to be affected by a mind-affecting effect, such as the Bard's Inspire Courage. Neat! ^_^
BUT WAIT! THERE'S MORE! Rules Lawyers will argue that willingly accepting the spell's result is contingent on foregoing the saving throw. They'll argue that since there is no saving throw offered, there is no saving throw to forego, and thus the "willingly accept" part cannot be triggered (it is an AND clause, after all). Also, this mentions a "spell", which Inspire Courage, being a supernatural ability, is not. From this point of view, all Undead cannot be affected by Inspire Courage.
Take that as you will. I'm just providing different POVs. ^_^