Is it possible to store a Windows Server user account in access table and have an application call those credentials to authenticate against a protected system?

Search this forum (and Google-search, too) for WinSock functions and SSL functions. As it is written, your direct answer is NO, it won't work automatically. Normally, this is a Windows function, not Access. But hey, when you have VBA and a couple of DLL files to provide interfaces, who knows?

I want to authenticate against local credentials.

I have two domains in which there is no trust between them. Basically a local domain and DMZ webserver. I want to store the credentials of a local user from the webserver in the database located in the local domain so that the database would use the store credentials when accessing drives/data on the webserver.