Many, I believe. Without borders, people would be allowed to move freely to the areas with the best opportunities. With the borders and immigration rules as they are, many people are deterred from moving and seeking different options. Moving to a different country, gaining citizenship, and becoming employed is a long, expensive, and difficult process. Many countries also do not allow migration without a citizen sponsor and/or immigration lawyer, which further complicates the process. If there were no world borders, I believe almost every person in the world would seek a setting where they were offered the best and safest opportunities, regardless of location.

In some cases, such as South America, the US, and the East, many more may choose to leave than are currently as they've been stopped by border limitations. However, if you were to take the European Union, for instance; there have been open borders for many years and hundreds of millions have chosen to stay in their country of choice as opposed to the handful of millions that have, in fact, left. Of course, it depends on the state of the country; if you're living in a wealthy country where you can easily get a good job, of course you'll stay, whereas you'd be tempted to leave if you were in a worn-torn country. Generally, if the country offers a good standard of living, in the larger scheme of things, few choose to leave said country. There is also a generational gap. Older generations seem to have a desire to stay in their native country (the UK and Spain is an exception) whereas younger generations leave early and, often, take their family with them. People are only choosing to leave if they are in a problem country; much fewer Norwegians, who are known for their excellent quality of life, choose to leave when you compare figures to India, for instance.