Well, duh. That is the very intent and design of gun control laws, to give people who want to acquire guns a "harder time".
But this "study" which observes this entirely obvious point does not "back gun controls" as the title implies. For a study to "back gun controls" would have to mean, I would think, that the evidence and data found in the study would support the statement, "Gun Control Laws Should Exist".
But that statement flies in the face of the Constitution, of course; in particular, its Second Amendment. According to the Second Amendment - pending further data - it is clear that Gun Control Laws Should Not Exist.
So unless this "study" has found evidence that the Second Amendment does not exist or is otherwise fraudulent, it is entirely incorrect and misleading to say that the result of this study "backs gun control". Certainly it backs the statement "gun control laws make it harder for people to get guns".
But that statement by itself does not "back gun control".