What you are describing is made by purpose. User must know that TestComplete is waiting for an action from him, and there must be a way to let TestComplete know you've finished the action, that's why you have to switch back to TestComplete and click OK. The simplest solution here is to change the message in TC to something like "Switch to the browser, do bla-bla-bla, then switch back to TC and click OK button".
As for the your idea with Indicator, it will also work. To wait the page, you can use Browser(...).WaitPage method. The code would look like this:
while(true) {
if(!Aliases.browser.WaitPage(...).Exists) {
aqUtils.Delay(1000, 'Switch to browser and navigate to URL...');
}
}
The delay is required in order not to load the CPU too much.
Also, the provided loop while(true) is a bad example (since it is an infinite loop). I suggest using timeout to exit such loops after waiting too long (e.g. the test is run automatically on a weekend and there's nobody in the office to perform the actions required. You can have a look at the HISUtils.StopWatch object to learn more about timers.
And finally :). I don't know your specifics, of course, but requiring action from a user in automated tests is considered as a bad approach, try avoiding it if you can.
