In my own multiple (and recent) readings of the complete novels and stories of Sherlock Holmes, I see Holmes noted for a direct, rather dry style of verbal delivery. Watson, the narrator in this passage, has a more romantic cast on his interpretation of events, but also tends to stick to the facts, as he sees them.
I can't rule out the possibility of "Reading" being a play on words, but the lack of puns in the rest of the Canon would make it unlikely, perhaps even unintentional.
There is an immense amount of material written on all facets of the Sherlock Holmes stories. The following blog, http://www.sherlockian.net/ is just one of hundreds of examples.
I found one source directly pertinent to this question:
How much wordplay is in the "Sherlock Holmes" stories by Arthur Conan Doyle?
Karen Murdock has been studying the various figures of speech and rhetorical techniques in the 60 Holmesian tales, collectively called "the Canon". She notes a use of zeugma when Watson reports in The Hound of the Baskervilles: "All afternoon and late into the evening he [Holmes] sat lost in tobacco and thought." ("Lost in Tobacco and Zeugma", Canadian Holmes, Summer 2004, p. 3).
Murdock notes that puns and other humorous forms of word play are not found in the Canon.
However, that doesn't mean that there is no intended pun here. Personally, I believe it likely that it IS intended, however rare other such Canon examples may be, simply because authors tend to use words with a purpose.