Is the Law of Excluded Middle an allowed argument in court?

Yes, but admissibility does not imply conclusiveness. The former is a procedural matter whereas the latter is an issue of epistemic nature.

The scenario you outline seems inconclusive because the three premises fail to bridge the gap between the state of the phone and Alice's cognitive state. Two examples are:

• The conditional character of premise #3 renders it unclear whether Alice managed to reach Clare.
• Alice's state of mind (such as being sleepy, drugged, distracted, overwhelmed, etc.) could prevent her from grasping, or even paying attention to, the news.

Other obvious gaps are left out because you intended the scenario to be a simplified one.

Accordingly, in this scenario the law of excluded middle is inapposite on epistemic --rather than procedural-- grounds.

Does the burden of proof change anything (i.e. whether this argument is made by the prosecutor or not)?

Generally speaking, being plaintiff or prosecutor makes no difference in that regard. Furthermore, the burden of proof would switch to the defendant if he raises an affirmative defense that centers on that issue.

Is the Law of Excluded Middle an allowed argument in court?

Yes, but admissibility does not imply conclusiveness. The former is a procedural matter whereas the latter is an issue of epistemic nature.

The scenario you outline seems inconclusive because the three premises fail to bridge the gap between the state of the phone and Alice's cognitive state. Two examples are:

• The conditional character of premise #3 renders it unclear whether Alice managed to reach Clare.
• Alice's state of mind (such as being sleepy, drugged, distracted, overwhelmed, etc.) could prevent her from grasping, or even paying attention to, the news.

Other obvious gaps are left out because you intended the scenario to be a simplified one.

Accordingly, in this scenario the law of excluded middle is inapposite on epistemic --rather than procedural-- grounds.

Does the burden of proof change anything (i.e. whether this argument is made by the prosecutor or not)?

Generally speaking, being plaintiff or prosecutor makes no difference in that regard. Furthermore, the burden of proof would switch to the defendant if the defendant raises an affirmative defense that centers on that issue.