The question is
Can desire without the attachment still lead to suffering?
We have at least one concrete example of a negative answer to this question, from the Theravāda tradition which is the case of dhammachanda - desire for the Dhamma. This kind of desire, does not result in attachment or suffering. Quite the opposite. There is also the desire for the well-being of others that is such a vital part of Mahāyāna Buddhist practice.
It is certainly possible for someone to experience the attractive aspect of a sense experience without trying to grasp it. We do not noticeably grasp after every single pleasant experience we have for example. Some simply come and go. But the tendency which associates happiness with pleasant sense experience runs very deep and in practice we are usually grasping after some pleasant experience - trying to prevent it ceasing, or trying to recapture it through repetition. So desire without attachment is in fact extremely rare.
In the Theravāda model of the fetters, desire for sense experience (kāmarāga) is the 4th of the ten fetters (saṃyojana), but more subtle kinds of desire also exist, 6th is desire for material existence (rūparāga) and 7th is desire for immaterial existence (arūparāga). A once returner has weakened the 4th and 5th fetters; a non-returner has broken them, but is still subject to the more subtle forms of craving. Only the Arahant is entirely free from craving.
Mahāyāna Buddhists use a different model - the ten bodhisatva bhūmis. As one progresses through the bhūmis or "levels". The first bhūmi involves a very strong desire to help all beings to be liberated (bodhicitta). Since bodhicitta involves a direct experience of śūnyatā or emptiness, even the beginning bodhisatva is already free from the grosser aspects of desire. Through success stages the bodhisatva purifies their mind and their karma, through the practice of the six perfections, until they are completely free of any negative mental events.
Note that the two models are almost complete unrelated. Sometimes answers to questions like this are given in strongly sectarian terms - as though, for example, the Theravāda model is the only possible way of seeing the answer. For Buddhism as a whole this is always a distortion - sectarian views are seldom representative of Buddhists as a whole.
What we find in practice, however, is that these models are highly hypothetical and theoretical and can be entirely unrelated to one's experience of progress in the spiritual life. If I may be permitted an anecdote from my own life, I used to eat meat. I even worked in a butchers shop when I was a student (mostly cleaning, but also making small goods like sausages). I loved eating meat. But later when I discovered Buddhism I took on being a vegetarian, at first for ideological reasons, then later because I came to love animals. More than 20 years later I now never crave meat. I am entirely cured of any desire or attachment to eating the stuff. I find the very idea disgusting. I never knowingly eat anything that has or had neurons. Even if I was to cease being a Buddhist, I cannot imagine ever eating meat, except perhaps in the direst emergency (I feel about meat the way most people feel about cannibalism). So it is entirely possible to break some attachments, while still operating in a mode which is underpinned by patterns of desire and attachment.
One can gradually reduce the amount of desire one experiences - especially, I think, as one gets older and the blood cools. And as far as I know, there is no discussion of this phenomenon in any Buddhist text. Buddhists tend to present desire in terms of idealised models involving desire being an all or nothing proposition. I think we need to be wary of any kind of absolute, or any opinion stated as "Truth". We Buddhists all too often seem to fall for our own propaganda.