I don't know the full answer, but when we had compulsory military in the US, we required registration of those immigrants who took permanent residence. So back then we would have made a man of military age register and serve if he came to stay. Israel does this too, and still has compulsory service so if one moves to Israel one must be prepared to serve in the military.
As far as refusal of a potential immigrant. We are operating under the immigration act of 1965, sponsored by Ted Kenedy, and this specifies that the ratio of immigrants must be representative of the prior years admissions. Therefore, I am not sure the govt of the US will take "just anyone who shows up". I know Boxer (Sen from CA) has passed special admission criteria for people fleeing repression in some countries, like San Salvador. I know we have a special immigration policy for Cubanos who reach our shore. I am speaking of "permanent entry" as for visitors entering as tourists, no, we don't restrict anyone except persons on the terrorist lists.
I don't know what if anything the US would do if an Israeli (fleeing military service) wished to immigrate to the US. I suspect He would be denied because he is not from Asia, Mexico, or one of the repressed countries of Barbara Boxer. But my knowledge of the subject is unclear.
I did not mean to besmirch Canada and their policies, You have a present US deserter from the military, and so far he is not being sent home to face the music. He volunteered for service before he changed his mind. Back in the '60s, the Vietnam war was not highly supported and Canada offered an escape. I had friends who suggested I could consider this too if I were drafted. I was not. The radicals of that time do indeed have too much to say in government, here as well as Canada.
And they are definitely ruining Canada with their left leaning and multicultural approach to Canadian society.