Temp variations don't matter much in most cases. If the variation skews towards quite low the cook can take significantly longer. Cook time variations with more normal time ranges can occur if temp variations occur.
Temps variations during higher heat cooks might cause some issues if rubs are used, especially those containing sugar. Sugar caramelizes in the 320s, burns > 350. This does not mean that temps of, say, 365, 375 or even higher automatically create problems. Meat surface temps will be lower than ambient cooktemps because of evaporative cooling. However, if cooking continues at these temps for a while, surface moisture does dissipate and increases the likelihood of sugar burn.
As to your other question, I don't monitor meat temps for barbecue. If I am cooking to a low internal, say, for beef loin or knuckle cooked to medium-rare, or pork loin to the 140s, or the like, then I will monitor temps after cooking has gone on for a while.
Though I am not one of them, many cooks monitor meat internals during barbecuing because they find them useful in giving them an idea when to check for done. Internal temps of any given heat do not cause done - but they can correlate with it. To know barbecue (brisket, chuck, butt, ribs) is done, i.e., tender and juicy, it is best to check by hand and eye. A temp won't tell you this.
