An open question, not critical but elucidatory - by 'sentiment' do you mean feeling in the sense of 'emotional reaction'?
If so, then you might be asking one or both of two things:
1.Is there a common and distinctive emotional reaction that we have to all and only art?
2.Is it possible for art, recognised as such, not to educe any emotional reaction at all?
Common and distinctive emotional reaction?
It doesn't seem to me that when I experience an emotional reaction to art, considering it only as art and bracketing out any ethical, religious or other dimensions, I have an invariant kind of emotional reaction to different types or instances of art. For example, when I read certain lines from Shakespeare's 'The Tempest' I certainly experience an emotional reaction. I find it hard to specify this reaction; perhaps I can best express the experience by saying that it is a response to a perfection of fit between language and imagination.
Now, whatever can be made of that, I want to say that the experience it describes is - to swing examples - nothing like my emotional reaction to the two-dimensional images of ancient Egyptian wall paintings. These I recognise as art, yet it is (I think) the shapes and symmetries that produce the reaction here.
But the reaction is different in kind. I can find no commonality or sameness in the emotional reaction I experience in reading Shakespeare and the emotional reaction I experence in viewing the wall paintings - let alone a commonality that is distinct from my emotional reaction to non-art.
No emotional reaction?
I think it perfectly possible to experience something as art without any emotional reaction at all. I would not deny the status of art to conceptual art, taken here as exemplified in artifacts imbued with ideas (a characterisation that begs for more clarification, I readily admit), but it provokes no emotional reaction in me so far as I am aware.
Maybe I have misinterpreted the meaning you attach to 'sentiment'. If so, this is an honest mistake and its exposure might at least help to bring your question into clearer focus.
Note that I have said nothing here of art as expressive of emotion - the Croce/ Collingwood approach. I have kept to the observer's emotional reaction, which is a separate topic from that of whether art is expressive of emotion or not.
Damien Freeman, Art's Emotions: Ethics, Expression and Aesthetic Experience. ISBN 10: 1844655121 / ISBN 13: 9781844655120
Published by Routledge, 2011.
Jacques Maquet, The Aesthetic Experience: An Anthropologist Looks at the Visual Arts. ISBN 10: 0300041349 / ISBN 13: 9780300041347. ISBN 10: 0300041349 / ISBN 13: 9780300041347
Published by Yale University Press, 1988