A lot of people don’t advise Complex builds for any nation other than Japan (and that one is typically on the mainland in order to speed up the tank rush to Moscow) but I personally enjoy playing them much more than that.
Added ICs on the board change the focus and flow of things, shatter existing set strategies, and provide new and unusual paths for units to arrive at the front. On the downside, they also cost alot, are vulnerable to “free” bombing until you can man them with an AA gun, produce less than your starting Complexes (generally), and will come back to haunt you if your enemy takes them over and starts pumping out units.
That being said, with UK I’ve built complexes in India, Australia, South Africa, Anglo-Egypt, and a captured Norway with varying degrees of success. India and Norway seem to be the most stable of those. Egypt is fun but extrmely difficult to hold and you won’t get many units out of it - you almost need to put one in South Africa first, then build the Egypt one once you’ve got a flow of troops heading north to protect it.
Australia is a bit weak but if you condense the Indian/Australian fleets you can protect it OK and generate a decent island-hopping force - Japan will be big trouble for you but you will certainly garner some of their attention, which is good for Russia and the US.
Schedule? As soon as the situation and the economy alow it. I’ll put one in India UK1 or UK2, and the Norway one as soon as I’ve captured it and am sure that Germany won’t immediately take it back.