Based on my (quick) read of some articles on the subject, I would suggest that he drew at least some form of map, though not necessarily something worth preserving in a book for posterity.
My reason for suggesting this is that he proposes different methods of map projection. My take would be that, where the coordinates and maps and whatnot that exist in all of the known copies of the work are of unknown provenance, we can be relatively certain that the core ideas of a coordinate system and map projections probably came from Ptolemy. Those two novel inventions are the cause of the celebrity of the work more than the actual list of locations that comes along with it.
And while, granted, it may be possible for someone to work out how different map projections will look entirely in their head, just using visualization, I would really expect the person to take a few sample locations that, for example, outline Europe crudely, and then use the map projection math to plot those locations and see how it looks.
From there, once he’s certain that the method works correctly and will produce an outline that wouldn’t look completely unfamiliar to someone who had seen earlier, non-coordinate system maps, he might hand the list of coordinates and the instructions over to some servant or student to do out proper and fancy, maybe using the simple version he made as an example, adding another dot or two for the pupil, before sending him off.
This isn’t to say that he might not draw a complete map himself. I’m just suggesting that it would be unlikely that he wouldn’t at least produce a minimal proof-of-concept by his own hand, just as part of working the whole system out.
If we can trust that all three projections are original to Ptolemy, then I think that would be even more certain, since it would demonstrate that he did in fact have to put things down on parchment before he could get a sense for how it would look, and used it as a method for iterating on the design of the system.