First of all hhttps://path_to_file/..
is an URL, conversationally termed a web address is a reference to a web resource that specifies its location on a computer network and a mechanism for retrieving it. A URL is a specific type of Uniform Resource Identifier (URI). HTTP protocol enables/allows the client application (usually a web browser) to create HTTP requests containing the name of the web site it wants to contact for information exchange.
chromedriver executable location
In Troubleshooting - ChromeDriver it is mentioned that,
The path to the chromedriver executable must be set by the webdriver.chrome.driver
system property and the chromedriver binary must be in the system path.
So, Selenium's client expects the WebDriver executable to be in PATH
i.e. the location of the WebDriver executable to be added within the OS native PATH
variable.
Conclusion
So it can be concluded that it won't be possible to store the WebDriver executable within GitHub and use it in different projects.
trivia
Even WebDriver executable e.g. ChromeDriver or GeckoDriver won't get initialized if they are accessed from a network path. You can find a detailed discussion in CreatePlatformSocket() returned an error: An invalid argument was supplied. (0x2726) when trying to access chromedriver through network path