How can I display an element only if any value has been selected from an entity select field?
Got it! You need to check for a value greater than 0. 
user:
  '#type': webform_entity_select
  '#title': User
  '#multiple': true
  '#target_type': user
  '#selection_handler': 'default:user'
  '#selection_settings':
    include_anonymous: false
    filter:
      type: _none
text:
  '#type': textfield
  '#title': Text
  '#states':
    visible:
      ':input[name=&quot;user[]&quot;]':
        value:
          greater: '0'

I guess in PHP that must be:
$form['text']['#states'] = [
  'visible' =&gt; [
    ':input[name=&quot;user[]&quot;]' =&gt; [
      'value' =&gt; [
        'greater' =&gt; &quot;0&quot;,
      ]
    ]
  ]
];