No,The president’s power over refugee admissions is vast. He has the power to restrict visa issuance and entry of aliens to the United States. Obama also restricted visas for refugees, which basically went unquestioned. To go back further there has been a long standing restriction on travel to and from Cuba. You see a refugee or for that matter anyone from another country have no right under the Constitution to enter the US, and the US has the right to refuse them entry for any reason, even if it's discriminatory. So yes it's Constitutional, even though I disagree with it.
"Whenever the President finds that the entry of any aliens or of any class of aliens into the United States would be detrimental to the interests of the United States, he may by proclamation, and for such period as he shall deem necessary, suspend the entry of all aliens or any class of aliens as immigrants or nonimmigrants, or impose on the entry of aliens any restrictions he may deem to be appropriate."
gives him that power. So unless the supreme court rules this code is unconstitutional, the president has the power and thus it would be constitutional.