If your baseboard has no profile and is a simple board, then a butt joint on inside corners is, in effect, a cope so nothing wrong there. The issue I see is that your baseboard is thicker than door casings. Usually it's the opposite such that the baseboard dies into thicker casings, but to each their own . MDF paints great but you'll need to pay attention to sawn edges, you may want to sand and paint those before installation. Now that I think of it, mdf does not tolerate moisture well, so you'd be well served to prime all 4 sides before installing , particularly the edge sitting on the floor. just in case you do occasional mopping. I'm sure you'll do fine, good luck.