It depends on the difficulty of obtaining Y relative to its pleasantness, but in general I would say yes. Specifically, good anti-akrasia measures are valuable enough that you should be willing to go through quite a bit of effort to persevere them. Thus if the effect of obtaining Y in these circumstances is to persevere your precommitmint ability and than it is worth going expending a large amount of effort on Y. But, you should also keep in mind the possibility that you will develop a negative association between fulling your precomintmints and then having to go through a large amount of effort for a reward that isn't worth it. Is their some "guilty pleasure" or other suitable reward that you could substitute for Y, that would be keeping in the spirt of the bargain you made with yourself?