Can I take a laptop in my carry-on luggage and another laptop in my checked baggage, so that I don't have to pay customs duty for either of the laptops?

No

The duty free allowances are per person, not per suitcase.

It doesn't matter if one device is packed in your carry on luggage and another in a checked bag, you have to declare the contents / value of your combined baggage.

Does Indian Customs check the combined luggage of every person to see how much electronic goods they are carrying?

Probably not of every person and not all the time.

Like many customs authorities they depend on passengers making their own customs declaration and self-assessment and they have a "Green channel" for passengers to that not have dutiable goods and a "Red Channel" for passengers that do.

That system gets enforced by "random" more thorough checks and the fact that passengers getting caught walking through the Green Channel with dutiable/prohibited goods are liable to prosecution/ penalty and confiscation of goods.

As far as customs is concerned, there is no difference between checked baggage and carry-on baggage -- you go through customs after collecting your checked baggage. So your question about combined luggage makes no sense.