It will actually cause double entries in your database. What you could probably do is slow the script down so the database connections close off before it proceeds to the next step. The refresh rate is controlled at line 1714 of threads_import.php with this:

setTimeout("window.location.href='$url';", 1000);

That 1000 is basically 1 second. You could bump that up, to slow it down a bit to see if that helps.

You could also ask your host if there is a way around that. Some hosts have a staging area, not production, and possibly they could copy your site/db to the staging area that doesn't have this limit in order to do the import.

It appears that max_connections is set to '100000' That's a pretty high value, so I'm guessing you're on a shared server and it's pretty busy. Because the import script definitely won't use that many connections by itself.