Does this improve flavor somehow?
Yes. In cheese, slow is almost always better because it leads to a smoother transition between states. Slowing down acid production helps form additional flavor and aroma compounds. And more importantly, it slowly works on the casein bonds, gently breaking them apart in preparation for the enzymatic phase.
Does the acid level drop faster on heating the milk to temperature?
Depends on the amount and type of inoculant. You could use .1% FD, for example, which doesn't make much of a difference to pH. Or you can use a fast acidifier that would drop acidity off a cliff once it hits 6.2.
Could there be any negative effects from doing this?
May be harder to control acidity targets and texture targets, especially as you are dialing in amounts and culture types for your milk.
Would it be okay to try on most any cheese make?
What would be the flavor difference with doing this versus doing a mother culture?
A mother all it really gives you is live, happy, active cultures right away for a faster pH drop and faster make. A slow acidification gives you more even casein degradation right away (generally improves paste properties), and also forms additional flavor and aroma compounds.
There's one other benefit, which is that for some strains of lactic bacteria, they will inhibit pathogens and psychrotrophs, decreasing fat breakdown in raw milk and preserving its quality. But that is strain specific.