Watson has requested the presence of Holmes. Will Holmes go immediately? Why? (chapter 10-12)

Yes, Holmes appears in Chapter 12 after Watson notes that he is needed. Holmes, of course, always intended to be there. His "blackmail" business was a ruse.

But how in the name of wonder did you come here, and what have you been doing? I thought that you were in Baker Street working out that case of blackmailing.’

‘That was what I wished you to think.’