Yes, of course it would. Common sense dictates whom we invite into our own homes, and for we citizens the entire USA is our home.
In any group of say 1000 human beings, they will range from being very good people to very bad people, with the majority falling somewhere in the middle.
Regardless of what we are being told, it is nearly impossible to properly vet everyone wanting to come to our country. In many cases, there just are no records available to review on many of these people.
We also need to consider cultural differences which we are finding to be vastly different. Actions we in the USA would consider to be in violation of our way of life are considered acceptable and perfectly normal in the immigrants home culture. For instance, we know for certain that Muslims view females in an entirely different way than we do in our culture. They also prefer Sharia Law which we view as barbaric and brutal.
Most new immigrants to our country make no effort to assimilate into our society and segregate themselves into communities of their own kind. In some areas of the country we now have "No-Go" zones where our police officers are forbidden to go. I have no idea what idiot approved something like "No-Go" zones on US soil, but he or she belongs in a mental institution.
Would anyone allow a group of strangers to move into the basement of their home with the promise they would never check on what they are doing down there? I don't know about you but I wouldn't allow this.
In summary, even if we were lucky enough to get some detailed information on an immigrants past history, we have no real concept of the cultural differences we will be facing. This entire immigration issue has turned into nothing but a political football for our Politicians to leverage their way into office, or be allowed to keep their present position. There is nothing positive about this that will make America a better place for we citizens.