Yes With an If, No With a But
Other answers have suggested that live, fast-growing, barely conscious, human infant clones are not worth doing, because there are better methods which are less ethically fraught, better targeted to the required need, and less wasteful of resources.
Speaking practically, however, yes it could be done. But from a story-telling perspective, you might want to explain why it's done this way. You might have to explain that scientific advancement is at this very specific level where they can clone entire humans but [choose to?] not clone individual organs or use donor animals. (I don't know if one is "easier" than the other.)
Let's Do This
Maybe you could say your society is better at other bio-sciences than genetics. E.g., Maybe the "clones" are actually twins, created at the parents' request (or by the State, or by their employer) by splitting the "original" zygote into one or more separate zygotes, and one grows normally while the other(s) is harvested and given the "clone treatment." Maybe the fast-growth is done using synthetic hormones instead of gene-manipulation. Maybe the insensitivity to pain and low brain activity is done by lobotomy on the fetus, or chemically induced partial-coma.
Don't Look Here
On the other hand, your audience might not question the premise. E.g., on Star Trek TNG, Lt. Cmdr. Data cannot use contractions. He just can not. Trekkies ask why but then just figure "Oh it's complicated" and move on (or keep ranting till they die lonely). But if you're going to explore all the dilemmas that arise from your particular type of organ bank, audiences may wonder why we are doing it this way instead of all the other better ways suggested in the other answers.
But you might side-step the sci-fi dilemmas by re-directing attention to more legal and philosophical problems. E.g., is the clone property of the patent holder who invented the cloning process? Why would parents or individuals permit clones or even care? Etc.
But then we're back to where we've started: what issues are highlighted by these clones, which haven't already been explored by androids, replicants, zombies, sentient AI, and yes, clones? I'm not saying there aren't any such issues, I'm just saying that if you're going to set up a highly specific premise, then it should ideally be for a good specific reason. So, from a story telling perspective, it's hard to tell how practical this would be.