There is a single acount testimony of his sister in law, Bridget, that he was staying with his brother Alois in Liverpool, between 1912 and 1913 to avoid conscription.

While there is no way to disprove her claim, it seems unlikely that Alois would want to shelter his brother from conscription, or that Adolf would even need to run away across the continent to avoid being conscripted. For one, Hitler's relationship with his siblings was a shaky one at best, and he did not have to leave the country to avoid draft, just Vienna. Moreover, by that time Hitler became so sickly and frail that he would fail physical exam on conscription, even if he wanted to join the army.

Moreover, only year later, Hitler volunteered to join bavarian army instead, so the claims that he wanted to run away from conscription are not well founded.