WASHINGTON — The partial government shutdown over President Donald Trump’s demand for a border wall is playing havoc with the nation’s already backlogged immigration courts, forcing the postponement of hearings for thousands of immigrants. For some of those asking for asylum in the U.S., the impasse could mean years more of waiting — and prolonged separation from loved ones overseas — until they get a new court date. But for those immigrants with little chance of winning their bids to stay in this country legally, the shutdown could help them stave off deportation that much longer — adding to the very delays the Trump administration has railed against. “It is just dripping with irony,” said Sarah Pierce, policy analyst at the nonpartisan Migration Policy Institute.