It won't show on the Summary dialog of the planet (unless the effects are rolled into the totals at the bottom), but look in the upper RH corner of the Details page. If the SB is in range you will see the 14% Starbase bonus listed. And that bonus does affect the output.
Note that the displayed output is the base output, multiplied by the 1 + (SUM of the bonuses), multiplied by the Economy slider setting, and probably a few other things. Let's say you have a base output of 88, with existing bonus of 50%, for a gross output of 133. Times the slider value of e.g. 30% yields 40.
Now add 14% bonus. Gross output 144, times the slider value yields 43. So the effect is +3 rather than the +12 that you might expect from multiplying 88 * 14%.
But to answer your question directly, heck yes Economy starbases are useful! But they do eat a lot of production to get up, running, and protected, so I generally build them only where they can boost 3 or (preferably) more planets, barring a special case. And I don't protect them with modules unless there is a lurking threat.
To test this, crank up the game. Note the outputs on the planet page. Destroy the SB, then run a turn and note the outputs again. Quit without saving.