That may well be an issue - after all, Turkey has a large number of illegal immigrants from some countries to the east and south of it, and many of those people are no doubt aiming at the EU. But of course, visa concessions or visa-free access to the Schengen area/EU for Turkish citizens would neither increase nor decrease the movement of illegal third-country immigrants into the EU.

At the present time, though (unrelated to all of that), the process for Turkish accession seems to be stalled, or at least to be on a go-slow. I also get the impression (anecdotal only) that a lot of Turkish people have cooled to the idea, partly no doubt an instinctive reaction to a perceived (and in many cases real) lack of welcome, partly also probably due to somewhat improved economic conditions in Turkey, and no doubt partly as a result of lots of other factors as well.