If the child becomes connected as a direct result of the risks that the visitors took, would the person who managed to connect themself to the child be obligated to remain so connected for the nine months that they have physically committed to - by placing themself AND the child into that situation?"
Basic answer:
Hell no! No rational person should or would anyone feel so obligated by an act of visitation to, as you put it, a "child [that] has no measurable brain waves to indicate any level of self awareness, No ability for thought, No sense of pain, etc." Sh*t sometimes happens when one takes on risk, and other times it does not. If one has done nothing wrong, one need not feel obliged to bear the burden of the misfortune resulting from one's well intentioned deeds.
Analysis:
Even when the outcomes are identical, the circumstances leading to the taking a risk and having it not pan out as hoped differ from those of one's deliberately committing to an action for the purpose of achieving the specific outcome.
Prior to undertaking a given action (or set thereof), A, for the purpose of achieving outcome, O, if one is clear thinking, one will identify the attendant risks of performing A and develop a risk mitigation plan that specifies what legal actions B, C, D, etc. one will follow (1) to prevent the associated risks from becoming manifest, and (2) to attenuate the impact of the risks in the event they materialize into reality.
One can think and say whatever one wants to say about the individual's election to perform A, thereby assuming the corresponding risk(s) of doing so, but so long as A is permitted, the added burden of A's risks in pursuit of O are merely additional costs of A, and that is not one's business but rather the business of the individual(s) who undertook A.
Though I'm not familiar with Judith's violin scenario, I can quite plainly see a
huge difference between the process by which coitus leads to conception and the sequence of events in the storyline you've presented. I don't know what makes you, or anyone, think I'd see the process flow you've depicted as an analogue for that of coitus, conception, gestation and birth. That is no minor distinction you've introduced into the allegory. Quite simply, a fetus does not exist prior to coitus, the act that corresponds in your story to visitation. Maybe someday I'll read Judith's allegory, but if/when I do so, I sure as hell hope hers is better structured than is yours.