Release 2.7.0 of TortoiseGit claims it doesn't support Windows Git older than version 2.11 anymore. But it still runs, in my case with Cygwin Git version 2.1.1 (which I can't upgrade yet). What functionality of TortoiseGit could there be that is expected to be broken?
First running old versions of Git are a security thread as those versions contain known security holes (that's also the reason why TortoiseGit dropped support for old versions).
TortoiseGit basically will still run with old versions of Git, however, for some actions TortoiseGit might pass some options which are not known to older versions of Git and these actions will fail (cf. https://gitlab.com/tortoisegit/tortoisegit/commit/7d65e4f55f28ecca370c15bfb48da2c931da5aed; e.g. TortoiseGit used merge -unrelated, --progress for submodule update command, commit amend with "reset time to now", look into the Git release notes when those features were introduced).
Btw. Cygwin Git is also not supported officially by TortoiseGit. Please also note, that Cygwin Git also does not pass the whole test suite on Windows... (cf. https://stackoverflow.com/a/32427897/3906760)