You'll be ok. You might want a finer grind just to make sure the end texture is uniform (to prevent that aforementioned problem with bits from different areas). You might want to experiment first with some store sausage to get an idea of what you'll get.
The grind shouldn't be a problem, they will be completely emulsified into a paste. The bologna will be a paste of beef and pork. The mortadella will be a similar paste but all pork and different seasonings with blanched fat cubes, black peppercorns and pistachios mixed in after emulsifying the paste.