People who live under Communist government generally approve of them. Although there are some dissidents, most people in these countries have bigger concerns than politics. For example, most people in the People's Republic of China approve of their leaders in Beijing. Reasonable people recognize that no country can be perfect.
Unfortunately, the only remaining Communist government around is in Cuba, where there are as many benefits as there are widespread problems with the system. The others collapsed into totalitarian dictatorship or became something far more twisted entirely, like the case is currently in North Korea. Overall, people across the world will probably not want to try the great experiment again.
In general, a majority of world governments aren't Communist. Therefore, most people don't approve of Communist governments. Those governed by a Communist regime may or may not have a choice but follow the tenets of Communism if speaking out against the government is banned. True Communism (AKA Marxism) doesn't have a government because everyone owns everything within the country as Karl Marx wrote about. Unfortunately, Communism is a perversion of Marx's vision and is nothing like the ideal set forth by the philosopher.
Preference falsification often occurs when people are afraid to reveal how they really real about an issue. In communist regimes before they collapsed people would pretend in public to agree with the regime. Then after the collapse of the regimes most people agreed it was good that they had collapsed. The reason is preference falsification. While at first most people agreed with it and expected it to work over time it became clear that it wasn't working but people pretend they liked it to avoid being thrown in the gulag.
There are some people who agree with a Communist government, as there are still communist governments set up in the world. Most people today though look negatively on a Communist government. They feel the people don't have enough say and rights in this type of government. Most people would pick democracy.
No, people do not approve of Communist governments, because they do not do an efficient job of creating wealth. People are not as happy in a communist society, because they cannot choose what they want to do for a living, and they cannot even chose what they want to believe. People in a free society have more choice and more happiness.