Answering to what extent they investigate is hard. The answer is a combination of the duty of the embassy officers to make sure travelers obey the laws and the screening time, as they have a lot of applicants to screen per day.
Governments do not generally exchange all detailed personal information according to privacy laws. If they did, a new datagate would blow up. But there are indeed a lot of private data bases that governments can buy for money, plus a few tax exchanges that I know of.
Cheating at interviews is relatively easy as you may still deny to have been more than 6 months in China, but if your current passport shows a Chinese visa with entry/exit prints, no officer is denied to check every single passport page to verify your documentation. On the contrary, if they find a record that you have been in China for more than 6 month you will probably be banned from that country for a long time.
I generally do not recommend ignoring the laws, but you have to know that, for example
- There has not to be a general Big Brother who watches us 24/7 and governments can inquire by inputting your passport ID
- Your public social media may tell a lot on you. No one prohibits officer to screen your Flickr photos and question you about them. For example, USA ESTA application already requires listing social media accounts, while disclosure of the passwords is a debated topic under the Trump administration
- If you appear in a FATCA/CRS tax report, there is hint that you may lived more than 6 months in a country. How would you justify that? CRS is done in European countries in my example
I could speculate on the existence of your name / DOB on any private record indicating that you may have lived more than 6 months in a country. I currently have no source so I won't expand speculations. Anyway it is not certain that they will eventually find out. But mind the consequences if they do!!!!!