Generally, the answer is yes. Placing the ball on a tee instills an extra dash of confidence and produces contact slightly higher on the clubface, which adds loft to the shot. (It’s important not to tee the ball too high, though, as this can cause an unwanted lifting action in your downswing.)
But there are golfers – usually good ones – who eschew the tee in certain situations. For example, when hitting a wedge or other short iron where the grass on the teeing ground is sufficiently plush to provide a perfect lie. They may also play the ball off the turf when a low shot, such as a knock-down into the wind, is called for. Very rarely will they play a mid-iron, long iron or hybrid without the aid of a tee, however.
To determine your best par-3 approach, experiment on the range by teeing up and hitting shots with various irons, then playing those same shots right off the grass.
You may decide to tee up the same club in some situations while playing it down in others.