Is relevant self-citation an effective way to promote your work?
The answer might depend on how you define "effective promotion", but there is scientometric research concluding that self-citation leads to more citations - crucially including more citations by others. Instead of a comprehensive literature survey (which I'm ill-equipped to write), I'll just refer you to one of the more important papers on the topic as an inroad to the field.

Studying citations to Norwegian scientists, Fowler and Aksnes: "Does self-citation pay?", Scientometrics 72, 427-437 (2007) found (non-paywalled version)


  that the more one cites oneself the more one is cited by other scholars.  Controlling for numerous sources of variation in cumulative citations from others, our models suggest that each additional self-citation increases the number of citations from others by about one after one year, and by about three after five years. Moreover, there is no significant penalty for the most frequent self-citers — the effect of self-citation remains positive even for very high rates of self-citation.