If a friend wants to visit Canada from Russia, would it increase the likelihood that my friend’s visitor visa application (by invitation) would be approved, if my friend first got a Schengen visa?
Travel history is what is considered in some visa applications, not merely issuance of a visa. If your Russian friend has never visited another country, with a visa or visa-free entry, then obtaining a Schengen visa may have little value.
An invitation to house and feed your friend could help; financial sponsorship, however, may not be favorable. The visa decision process takes into account many factors, and no one can predict the outcome.