The presence of interveners doesn't seem to affect an appellant's chance of success at the Supreme Court of Canada.
I took a look at 844 recent Supreme Court of Canada cases that proceeded to the stage in which there was an appellant (as opposed to applicant). There doesn't seem to be any discernible pattern in the data.
The cases considered, data and Excel files can be found at the end of this blog post.
1. There are only around 80 cases that are disposed of by the Supreme Court in a given year so the data above covers a fairly long time frame.
2. The appellant and respondent win percentages don't add up to 100% because there are some cases that aren't identified as an appellant win or loss (usually for some sort of procedural reason). This affects about 15% of the cases but probably doesn't make a difference to the conclusions in this blog post.
3. It seems that the Supreme Court never accepts a single intervener. I am not familiar with this process but I couldn't find a case that had only one intervener. I thought this might be a mistake on my part (and it might be) but it looks like there aren't any single intervener cases.
4. The majority of cases (62%) had no interveners.
You can download the data used to generate the graphs in this blog post and the Excel file that contains them here: .tab.txt and .xlsx files
Following publication of this blog post, Keith Rose sent me an academic study on the effect of interveners at the SCC (from 2010) that concluded there is a "... modest but significant impact of interveners on voting by the Court as a whole ...". The paper can be found on SSRN. Professors Green and Alarie provide two alternative (and more sophisticated) approaches for the task of measuring the effect of interveners.