The answer to your question is the pdm client wont do alot without the server side, kinda pointless to try tbh
yes you need to run the server part to create a vault, the vault is stored in a sql database, and yes you can have multiple users accessing the vault at the same time, you cant access the same file though.
The server components are required to create a vault. You can install the server components on the same machine as the client for testing purposes.
I've been asked to install the client without the server to see what it can do.
It will do absolutely nothing.
I understsand there is the server and client components, but is it necessary to run the server component in order to create a vault ?
Yes. but you can install the server component on any computer... it does not need to be a "server".
Assuming this is so, and the vault is stored in a common network accessible area, can two solidworks clients both access the vault concurrently ?
Actually, it's better practice to install the vault / server software on a server/computer that has restricted user access. The only way a user should interact with the vault is with the Client software. Depending on the number of licenses you have... you can have 1 or hundreds of users on the vault concurrently.
Keep in mind the vault is not simply network accessible storage space, it is a program... a SQL database that is running all the time.
Take a look at this Solidworks PDM Installation guide. It should be helpful.