I did some testing for this and what i found is the scheduled task would run, and the delay worked.
In Task Scheduler I could see it queued upon log on, and running a short time later.
I could see it running in process explorer.
The problem was the IE window was not visible.
This may be why it didn't work for you...
It seems "Run only when user is logged on" must be checked for the window to be visible. Why is a Windows 7 scheduled task running hidden? - Microsoft Answers
I logged in with my Admin account to set it up in task scheduler.
I set it up to only run when my STANDARD account is logged in.
So, I'm not sure if this approach is something you want to pursue, or it's too complicated.
It sounds like you are setting this up for a Business.
Does it need to run with ADMIN authority while logged in with a STANDARD account?
Will there only be ONE STD user account per PC that needs to run this?
If you don't need to run with ADMIN authority you could probably simplify this and just log in as the STD account and set up the scheduled task there.
I don't have access to a domain for my tests.
Also, it may be possible to set it up to run for a GROUP instead of a USER...i'm not sure
The screen prints highlight settings i used.