How can I check that an invite email has actually been sent

Welcome to the Community, @accounts528. 

We can use the audit log report to see your added users. The Audit Log feature helps you keep track of your activities. 

I'll show you how: 

1.  Sign in as an admin to access the audit log.
2. Go to the Settings menu, then select Audit log.
3. Choose the appropriate Names, Dates, or Events filter to narrow the results.

If the user is there and didn't received your invitation, the invitation might be in their junk or spam folder. If it isn't on the list, or the recipient confirmed he didn't received it, I'd suggest resending the invitation. 

Here's an article that will guide you with the process: What to do if invited users did not receive your email invitation in QuickBooks Online.

I'd be here to help you again if you need more guidance in adding your users to your QuickBooks company.