This is a "you'd have to ask them" answer. The earliest use of 'canary' with reference to computing that I could find is a bit suggestive, but only that.
On 21 July 2010, Albuquerque Journal (New Mexico; paywalled) reported that Sandia National Laboratories had won one of R&D Magazine's (R&D for "Research and Development") "Oscar of Innovation" awards for software called CANARY, "that immediately detects contamination by analyzing signals from networked sensors".
According to Wikipedia, on 22 July 2010, that is, one day after the Albuquerque Journal reported the award given to Sandia's CANARY software, "Google announced it would ramp up the speed at which it releases new stable versions...This faster release cycle also brought a fourth channel: the 'Canary' channel". The introduction of the "Canary" channel was evidently reported 23 July 2010 in a web page by Lee Mathews titled "Google drops Chrome Canary build down the Chrome mineshaft" (cited at Wikipedia but no longer accessible).
While the coincidence is likely to be nothing more than that, coincidence, it is possible the Sandia software and "Oscar of Innovation" award suggested the name for the Chrome release channel. You'd have to ask them.
My other results were negative. While 'Chrome' is 29th in the frequency-sorted list of collocates (at a distance of four or fewer words left or right from 'canary') of 'canary' in the NOW corpus (2010-present), 'software', 'release', 'version', 'channel' and 'program' do not appear in the frequency list of the top 500 collocates. None of those terms (including 'Chrome') appear in the list of the top 500 collocates of 'canary' provided by COCA (1990-2015).
Newspaper archive searches were also negative, although the 'canary version' is the name of one fictionalized version of an unsolved 1920s murder — a case which, I mention irrelevantly, engendered the term 'sugar daddy'. The 'canary version' was also the name given by a reporter to his flight of fancy regarding a 1933 production of "Il Signor Bruschino", "an early Rossini exasperation". Other mentions of 'canary' in US papers were equally irrelevant.