First, I created a list with 4,999 items and notice how it displays correctly within a web part on my SharePoint home page.
Now, I go and add 2 more items in my list to put the total above 5,000.
The list web part still displays properly on the home page.
I increased the list to over 6,000 items and I have had no issues with the list view web part on the home page. Continued to increase to over 10,000 items and the list continued to work properly.
So it appears from my experience that the list works properly - as long as the view is less than 5,000 items everything works properly.
I would definitely be interested in hearing from those with other experience on this.