Maybe, but you should consider the possibility that WI-Bob has other reasons that he doesn't articulate consciously: for example, "it's not just that I want to have fun right now, it's that I'm anxious about this particular task, I know I'll feel that anxiety when I'm working on it, and I don't want to face that right now" (to take one example). Bring this into the open, and the negotiation might look quite different. (E.g. are there ways to assuage the anxiety in advance? That might help.)
This sounds good in theory. But in my experience, WorthIt-Bob doesn't usually argue rationally.
I didn't say anything about WorthIt-Bob having to be rational... you've dealt with irrational people before, and you can deal with irrational sub-agents, too. Heck, you can even train your pets, right?
In particular, Orthonomal has some great advice for dealing with people and sub-agents alike: figure out all their feelings on the issue, even the ones they didn't know they had. Then they might turn out more rational than you thought, or you might gain access to the root of their irrationality. Either way, you get a better model for them, and you probably need it.
tl:dr; Dynamic consistency is a better term for "willpower" because its meaning is robust to changes in how we think constistent behavior actually manages to happen. One can boost consistency by fostering interactions between mutually inconsistent sub-agents to help them better empathize with each other.
Despite the common use of the term, I don't think of my "willpower" as an expendable resource, and mostly it just doesn't feel like one. Let's imagine Bob, who is somewhat overweight, likes to eat cake, and wants to lose weight to be more generically attractive and healthy. Bob often plans not to eat cake, but changes his mind, and then regrets it, and then decides he should indulge himself sometimes, and then decides that's just an excuse-meme, etc. Economists and veteran LessWrong readers know this oscillation between value systems is called dynamic inconsistency (q.v. Wikipedia). We can think of Bob as oscillating between being two different idealized agents living in the same body: a WorthIt agent, and a NotWorthIt agent.
The feeling of NotWorthIt-Bob's (in)ability to control WorthIt-Bob is likely to be called "(lack of) willpower", at least by NotWorthIt-Bob, and maybe even by WorthIt-Bob. But I find the framing and langauge of "willpower" fairly unhelpful. Instead, I think NotWorthIt-Bob and WorthIt-Bob just aren't communicating well enough. They try to ignore each other's relevance, but if they could both be present at the same time and actually talk about it, like two people in a healthy relationship, maybe they'd figure something out. I'm talking about self-empathy here, which is opposite to self-sympathy: relating to emotions of yours that you are not immediately feeling. Haven't you noticed you're better at convincing people to change their minds when you actually empathize with their position during the conversation? The same applies to convincing yourself.
Don't ask "Do I have willpower?", but "Am I a dynamically consistent team?"
The task of keeping your various mental impulses working together coherently is called executive functioning. To deal with an "always eat cake" impulse, some may be lucky enough to win by simply reciting "cake isn't really that tasty anyway". A more potent technique is to practice visualizing the cake making you instantaneously grotesque and extremely ill, creating a psychological flinch-away reflex — a behavioral trigger — which will be activated on the sight of cake and intervene on the usual behavior to eat it. But such behavioral triggers can easily fail if they aren't backed up by an agreement between your WorthIt and NotWorthIt sub-agents: if you end up smelling the cake, or trying "just one bite" to be "polite" at your friend's birthday, it can make you all-of-a-sudden-remember how tasty the cake is, and destroy the trigger.
To really be prepared, Bob needs to vaccinate himself against extenuating circumstances. He needs to admit to himself that cake really is delicious, and decide whether it's worth eating without downplaying how very delicious it is. He needs to sit down with the cake, stare at it, smell it, taste three crumbs of it, and then toss it. (If possible, he should give it away. But note that, despite parentally-entrained guilt about food waste, Bob hurting himself with the cake won't help anyone else help themselves with it: starving person eats cake > no one eats cake > Bob eats cake.)
This admission corresponds to having a meeting between WorthIt-Bob and NotWorthIt-Bob: having both sets of emotions present and salient simultaneously allows them to reach a balance decisively. Maybe NotWorthIt-Bob will decide that eating exactly one slice of cake-or-equivalent tasty food every two weeks really is worth it, and keep a careful log to ensure this happens. Maybe WorthIt-Bob will approve of the cake-is-poison meditation techniques and actually change his mind. Maybe Bob will become one person who consistently values his health and appearance over spurious taste sensations.
Or maybe not. But it sure works for me.