Yes.
That's how it works.
And the cool part is if you add a "clipping" on your iphone it will show up on your desktop.
the way it works is that you create a newsgator account that acts as middleman between you mac (or windows) , the iPhone, or in my case,
my mac, my iphone and my macbook air.
works gret 99% of the time, sometimes you will see something that you swear you read before but I am not sure that it is newsgators fault, it could be the web site updating a story (for a typo?) which then the newsreadwer would correctly consider as "new".
You can also "delete" feeds on your iphone which are either true deletes of that feed OR you can choose not to show it on your iphone which helps out a lot.
"Of if I mark all as read on the desktop keep it read on iPhone? "
you need to test that out. unsure about that.
It's all free though so give it a try.