I have my tongue pierced and have pierced others as well. You should never pierce your own tongue, many complications can happen and you may not be able to determine properly if your tongue is able to be pierced, due to vein placement many people cannot.
Yes you can and many other things could happen. Professionals are trained to be able to determine if your tongue is able to be pierced. A lot of people have been turned down when looking to get it done. There are many places on the body that can be pierced safely when taking proper precautions but the tongue is the one place you should never take the risk.