Will a master student publishing several short papers come across in a bad way?
Try it. It can't hurt.

Having published before starting a PhD program will be seen as an advantage by the people who evaluate your application. It certainly won't count against you, unless you publish in junk outlets and neglect your exams over it, which should be your priority.

This last sentence is important though. It's much more likely to produce publishable results in a BA project than in a term paper. So make sure not to make the perfect the enemy of the good. In the humanities, having one high-ranking publication before grad school is already very good.

In any case, aiming high but realistic will be seen as determined and ambitious, not as arrogant by admissions or your teachers, whom you should also approach for advice and feedback. How you will be perceived of course also depends on how you present yourself.