No they won't work
The redistributable package is a .exe, which installs the required DLLs
msvcrtXXXX.dll
Where XXXX changes per build (VS2017, VS2015,...)
It is also not reference counted, which means no matter how many people install it, one uninstall rips out the files.
UPDATE
The Visual Studio 2017 does not change the version number
VS2017 msvcr140.dll
VS2015 msvcr140.dll
VS2013 msvcr120.dll
VS2012 msvcr110.dll
VS2010 msvcr100.dll
VS2008 msvcr90.dll
Thus Microsoft believe that the VS 2015 and VS 2017 redistributable packages are compatible.
Unfortunately, looking for downloads of VS2015 and VS2017, they are both available, so there may be subtle differences.
If the 2015 does not install, it will be because it thinks it is less good than the already installed 2017. However I have failed to find strong documentation that this is what Microsoft expects.