Answering just your title question, I would say usually, yes.
In Canada, exceptions to copyright are characterized as user's rights and are not to be interpreted restrictively. In particular the categories of allowed purposes, including research and private study are to be given wide margins. Once the potentially copyright breaching action is determined to be for an allowable purpose, then consideration is given to whether the the action was "fair." Please see CCH Canadian Ltd. v. Law Society of Upper Canada, 2004 SCC 13 for further details.
This is a case-by-case analysis, but under normal circumstances, I would be surprised if the courts saw a single copy for private study as unfair.
[...] use of sites like Library Genesis [...]
Oh, this again. From what I understand copying from the site would be copying from an illicit source. This would probably weigh strongly against a finding of fair use especially on the nature of use and alternatives to use fairness factors (see CCH at paras. 57-58). That said, in my opinion the "single copy for private study" portion weighs strongly for fair dealing, so I would not want to hazard a guess on how those factors would balance out.
Fair dealing is only one exception to copyright though, and it's always worth checking the Copyright Act for other possible allowances. In this case I can only find one, the s. 30.71 temporary reproduction exception. Making a specific download would not be legal under this section, but mere use and regular browsing could be as your browser makes temporary technical copies to display requested content. However, as I've previously covered, Canadian law is currently unclear as to whether this exception can be applied to illicit sources.