In my opinion, no. Willing implies consent. However, a mindless creature, by definition, does not have the ability to make a decision. It is driven purely by instinct, and cannot do anything that requires thought or choice. For instance, mindless undead are specifically mentioned to be unable to take skills or feats. So, being unable to make choices, mindless creatures cannot consent to anything.
The corollary to this would be that it is equally incapable of withholding consent. Once again, this would require it to make a choice, which it is incapable of doing. This is an important distinction. It means that while a mindless creature could not be a willing subject for any spell that requires it, it also gains none of the benefits that might be afforded it for being an unwilling target. Mechanically, mindless creatures just don't care, and may not even be aware that the spell is being cast.
However, with that said, any ruling on this matter will be heavily dependant on Rule 0, even more than most. People's definitions of what it means to be mindless, and more importantly whether consent is assumed given or denied by default, vary widely. While I take the neutral stance of assuming that both consent and the refusal of same require an active choice to be made, some will assume consent unless it is specifically refused, and others will assume no consent unless expressly given. Still others will assume that any creature, mindless or not, automatically and instinctively accepts anything that helps it, and rejects anything that harms it, unless specifically stated otherwise or when "help" and "harm" are subjective. It doesn't really matter which is used, as long as they are used consistently. I simply offer what would be the most strict interpretation of both mindlessness and willingness.
This question offers more information on what it means to be willing, though I'll note that it still leaves the subject of a creature unable to give consent unclear.