If I close the smtp relay completely in Plesk will that affect the ability for user to send email to other domains not located on the server?

I want to disallow SMTP access for third party clients, i.e. outlook etc.. but want to leave ability to use webmail and scripts to send mail as is.

It is wise to disable relaying, which is an open invitation to spammers. This doesn't prevent legit users from accessing the mail server via SMTP unless you disable it.

What I am asking is how can I close off the smtp server from all third party clients even from customers? Yet I want them to have the ability to send mail with our server using webmail and scripts.

We have notified our customers that they will need to use their ISP's smtp...

It your webmail works by using sendmail or qmail on the server then turning off the SMTP server will accomplish what you want.

However it seems odd, as allowing scripts to use sendmail / qmail is less secure because sometime they can be abused by spammers, wheras SMTP requires a user account on the server.

The reason for shutting off client smtp access is because of weak passwords being guessed and expoited - plus most ISP's are now blocking third party smtp.

to accomplish that you would allow no relay domains besides 127.0.0.1 localhost , All mail from scripts / webmail originates from localhost / 127.0.0.1...