Yes, when test fails it will run after hook.

This code:

before("login to system", () => {
  console.log("BEFORE")
  throw new Error('error');
})

it('testing...', (done) => {
  console.log("IT")
  done();
});

after("delete the user", () => {
  console.log("AFTER")
})

Output this:

BEFORE
    1) "before all" hook: login to system for "testing..."
AFTER


  0 passing (14ms)
  1 failing

  1) States Get
       "before all" hook: login to system for "testing...":
     Error: error
      at Context.<anonymous> (test\index.js:22:11)
      at processImmediate (node:internal/timers:463:21)

Also you can check this github discussion: #1612 where here says:

Please see the example below, showing that after is correctly invoked after the beforeEach failure

The code

// example.js
before(function() {
  console.log('before');
});

after(function() {
  console.log('after');
});

describe('suite', function() {
  beforeEach(function() {
    throw new Error('In beforeEach');
  });

  afterEach(function() {
    console.log('afterEach');
  });

  it('test', function() {
    // example
  });
});

And the output.

// Test run
$ mocha example.js

  before

  ․afterEach
after


  0 passing (7ms)
  1 failing

  1) suite "before each" hook:
     Error: In beforeEach
      at Context.<anonymous> (/Users/dstjules/git/mocha/example.js:11:11)
      at callFn (/usr/local/lib/node_modules/mocha/lib/runnable.js:251:21)
      at Hook.Runnable.run (/usr/local/lib/node_modules/mocha/lib/runnable.js:244:7)
      at next (/usr/local/lib/node_modules/mocha/lib/runner.js:259:10)
      at Immediate._onImmediate (/usr/local/lib/node_modules/mocha/lib/runner.js:276:5)
      at processImmediate [as _immediateCallback] (timers.js:358:17)