Could you please let me know if Flash Player will inform a user that his system requirements are insufficient when trying to use a given version of Flash Player?

It depends, but in general, no. 

The guidance on minimum system requirements is mostly about what we will and won't fix bugs for.  Flash Player probably works on Windows Server 2000, and we're not going to intentionally break it or prevent you from installing it, but we're also not going to fix it if it breaks.  In instances where it's going to crash on launch or have some other horrendous out-of-box experience, like attempting to install on a PowerPC Mac, then we'll prevent the installation outright.