Based on the Austrian conscription law of 1868 and militia law 1886 only citizens could be conscripted.
The only exception would be for a foreigner to be conscripted would be with
- permission from the Emperor and
- permission of the government of the foriegner's citizenship
- with a minimal age of 20
base on the §§1,3,6 and 16 of the conscription law of 1868.
Since the United Kingdom declared war on the Austrian empire on the 14th of August 1914, it is unlikely that they would grant one of their citizens permission to join the Austrian army.
Even had they done so, it is unlikely that the emperor would have granted permission to a minor enemy foreigner to join the army.
To my knowledge, only the United States conscripts residents who are foreigners.
Since the first step of conscription was the checking for eligibility in the registry (where age and citizenship would be noted), it would be more likely that a UK citizen would be sent to Internierungslager Grossau, which is where English and French citizens were interned until 1917.
After the English and French who had, up to then been quartered there, were moved from Grossau on April 29, 1917, the camp was temporarily vacated on May 1, 1917. Among the internees was James Joyce's brother, Stanislaus Joyce, who had been transferred from the Kirchberg an der Wild internment camp.
Arrested as a subversive on December 28, 1914, at the beginning of World War I, he [Stanislaus Joyce] was interned by the Austrians at Katzenau, near Linz.