Even when the accelerando is not written in, it might be implied - the organist can speed up the tempo in places which carry developmental character and increase of tension. This comes from a German Romantic tradition to think in waves, such as in tides - the alternate rising and falling of the sea, hence crescendo and diminuendo or accelerando and ritardando.
But here's the thing - where is this boundary when the accelerando might begin to sound too hasty? In other words, when does your playing might show the signs of rashness?
I think you begin to feel the signs of hastiness when you stop listening, when you stop noticing what's happening in your piece and only are concerned with speeding up the tempo.
Such playing might appear deceivingly virtuoso to the untrained eye but deep down we all know that the performer is simply making a mess out of the composition.
There is no attention to detail here, only speed is the ultimate goal.
Make no mistake - when you fail to notice harmonic nuances, dissonances, modulations, and structural points in your piece (also when improvising), you will also fail to communicate the musical story to the listener that the composer encoded with these musical ideas.
Hence you will be remembered as an organist who plays fast and loud. We all have our examples of such players, don't we? And you don't want that to happen to you.
What you really want is to be remembered as someone who talks to the heart and soul of the listener through music.