Yes we can, Odoo 10 can handle Leave requests directly from the mail. for that, we can find a function named

_notification_recipients  in the hr_holidays model.

@api.multi
def _notification_recipients(self, message, groups):
    """ Handle HR users and officers recipients that can validate or refuse holidays
    directly from email. """
    groups = super(Holidays, self)._notification_recipients(message, groups)

    self.ensure_one()
    hr_actions = []
    if self.state == 'confirm':
        app_action = self._notification_link_helper('controller', controller='/hr_holidays/validate')
        hr_actions += [{'url': app_action, 'title': _('Approve')}]
    if self.state in ['confirm', 'validate', 'validate1']:
        ref_action = self._notification_link_helper('controller', controller='/hr_holidays/refuse')
        hr_actions += [{'url': ref_action, 'title': _('Refuse')}]

    new_group = (
        'group_hr_holidays_user', lambda partner: bool(partner.user_ids) and any(user.has_group('hr_holidays.group_hr_holidays_user') for user in partner.user_ids), {
            'actions': hr_actions,
        })

    return [new_group] + groups

There is also controller written to accept the validation/refusal through the link.

@http.route('/hr_holidays/validate', type='http', auth='user', methods=['GET'])
def hr_holidays_validate(self, res_id, token):
    comparison, record, redirect = MailController._check_token_and_record_or_redirect('hr.holidays', int(res_id), token)
    if comparison and record:
        try:
            record.action_approve()
        except Exception:
            return MailController._redirect_to_messaging()
    return redirect

@http.route('/hr_holidays/refuse', type='http', auth='user', methods=['GET'])
def hr_holidays_refuse(self, res_id, token):
    comparison, record, redirect = MailController._check_token_and_record_or_redirect('hr.holidays', int(res_id), token)
    if comparison and record:
        try:
            record.action_refuse()
        except Exception:
            return MailController._redirect_to_messaging()
    return redirect

Thanks.