Is it possible to learn and play some classic organ music like J.S. Bach_ Toccata & Fuga on a 88 key digital piano, after switching the sound generator into "organ" mode? There is only one manual, and the feet keyboard is obviously missing, but the range of the instrument seems comparable. An organ, even digital, seems rather expensive instrument.
There have been a few periods when organ music was written for manuals only, and some of it is playable on a single manual, especially if you can set up the keyboard so notes above and below middle C have different organ tone colors. Many 16th and 17th century English, French, Spanish, and Italian organs had either no pedals at all, or there were a few pedals which were only used to sustain long bass notes. English and Spanish instruments were often built with "divided stops" that could be independently selected on the treble and bass parts of the keyboard. In fact early English organ music would fit better on an 88-note keyboard than on a modern organ, since the compass of the manual(s)went down to G below the bottom C on a modern organ console.
Those four national organ-building traditions were very different from each other, and each had its own contemporary group of composers.
The above doesn't include the German organ building school, and the related Flemish and Dutch. There are pieces by Bach's predecessors like Reincken and Buxtehude (and even by Bach himself) written for manuals only, but not many, and most of them are not very substantial.
The harmonium (i.e. a single-manual reed organ, now often called an "American Organ") was invented in France in the middle of the 19th century, and several organ composers wrote for it, including Alain, Boëllman, César Franck, Karg-Elert, Liszt, Reger, Widor, etc. (French missionaries introduced the harmonium into India, where it was incorporated into "classical" Indian music as a drone instrument, and still used for that purpose!)
But as other answers have said, you can't play what a typical member of the public would call "organ music" on an instrument with one manual and no pedals, unless you make a piano transcription of it.
You have to distinguish between playing transcriptions of organ music and practicing for later playing of organ music on an actual organ.
The first was much in vogue in the 19th and early 20th century, when the church lost influence and keyboard virtuosos wanted to preserve the repertoire of the old masters (mainly Bach), without forcing their audience away from the concert halls to which they were accustomed. (Organs in oncert halls were not as prevalent then as they are now.)
Playing such transcriptions on a DP works about as well as playing anything else intended for grand piano. The difficulty is with the arrangements themselves, which are often much harder than the originals: you have to redistribute voices awkwardly to get them all sounded, and sometimes the arranger even introduced doubled voices to mimic the sound an actual organ would make.
Practicing for later playing on an organ works only up to a point. You can imitate the sound, but the playing experience for you (rather than your listeners) lacks the feel of a proper pneumatic or mechanical keyboard, and it's very hard to acquire the proper touch by playing exclusively on your artifically-weighted plastic keys. Also, playing with your feet as well as your hands is astonishingly hard for people used to piano playing, and no amount of pretence can make up for a large amount of practice on a real organ console.
In short, the one works passably well, the other lacks key ingredients that you really, really need to become an accomplished player. It's alright for previewing pieces to rehearse later (I do this myself occasionally) and maybe practice the manual part a bit, but it's no substitute for the real thing at all.
This will not solve the pedal issue. However, I as well have a digital 88. It's the Kawai MP 9500. Prior to purchasing, I visited music stores with scotch taped nickels that weighted down the keys to approximate more or less a Steinway. After 1 and a half years I did find the above mentioned keyboard in which the keys are wood encased plastic. It is a wonderful instrument. At least you get the feel that's close to a 'real' piano. I'm not sure, but I think there are some separate pedals available so you can play those notes thru an amp. Hope this helps.