Yes. In a real emergency there's not time for Congress to meet, debate funding, etc so the president should have the flexibility to address that until there's been an appropriate amount of time for Congress to meet. Failure of Congress to discuss the issue could be taken as implicit approval.
In this case, Congress did meet to debate the issue and decided it was not worth putting money there. Failure of congress to agree with you after debate does not make it an emergency.
Personally, I think it is ridiculous that a US President is able to unilaterally declare an emergency and then is able to veto a bill from congress that says "no, it's not an emergency". They should not be veto-able; it's giving the president too much power.
Except his example wasn't true. In the city in question (El Paso) the wall put up did not drive down crime.
No, border barrier did not bring down crime in El Paso