I am not affiliated to EMBL and can only tell you what I have heard from my collegues but from what I have seen it is totally possible, though it might be that you have a higher chance for doing 5-6 month / master thesis if they previously now you. Also, i think to remember that interships / stays over 3 month are paid in all EMBL locations. Though you obviously have to determine that with a supervisor. Here in Heidelberg, many students have gotten positions via networking / knowing PhD students working there etc, but some have also just asked for an opportunity and here and there are job offers, though not many.

The only thing I would consider in your position is why do you espacially want to EMBL? They are doing very interesting things but many other do too, especially if its "just" for 6 month. And if you especially want to go to Heidelberg there are many other bioinformatics labs too like at the DKFZ, though it could be hard to get an unpaid intership with the new minimum wage regulations. Master thesis though, should not be a problem.

Internships at EMBL are usually not advertised. Some labs take students, others not. Just contact the lab you're interested in. You'll find some info on the EMBL website here.