They can but not on their own will.
Rewarding does not necessarily mean "feels good."
I can't think of something experienced as a reward that feels bad. It wouldn't be a reward.
Goals can just be goals.
Are your goals to fail, be fired, starve, go broke, get sick, be killed, or hurt?
Goals of NORMAL people are to achieve that which feels good, your goals notwithstanding.
Desire≠values
That's novel. We desire that which we value; nevertheless, base don your arguments you may desire worthless, dead-end things.
A goal can also be the happiness or success of another, and we can sacrifice our own "feels good" for that goal.
They can but not on their own will [choose something for no reward whatsoever.]
This seems an extremely limited view of "will." A very limited will that is a slave to reward? It seems not conscious at all.
Are your goals to fail, be fired, starve, go broke..
Again, in isolation, no. But rather than what? Will you do absolutely anything rather than go broke?