This question doesn't make sense to me. These chimera would presumably be a species, whereas I would only fall in love with one individual. Whatever anatomical configuration they do or don't have, that would be a fundamental barrier to anything before one could consider the question of romantic entanglement. This question is meaningless.
Well, this just seems a bit like asking if we enjoy falling in love with destriers or rounceys. The more fundamental question is whether we could love horses at all.
After consideration, it almost has to be the top half as a fish. Any meaningful relationship or romance requires the ability to communicate. However, there are no fish with the necessary anatomy to articulate human speech. Likewise, their fins don't even afford the opportunity for sign language or other modes of communication. Yet, if enduring bonds are capable between these fish-people and us, they must have some other mode. I am forced to conclude that they are capable of telepathy. If that is in fact that case, that would be a greater and more meaningful intimacy than someone who can simply talk to you.
No it isn't. If that's the best you have I'm taking that as a no and reversing course. You have to be able to talk.