I agree - it should be fine.
The concrete floor will actually help keep the hens' nails short as they scratch about.
I'd suggest that you'll need to put some material down for them to scratch through. Things like bark aren't great, as they can hold moisture, which then leads to mould, and can make them poorly.
Whatever you put down (wood shavings?) you'll find that you need to dig it out an replace it every so often. Makes excellent compost :)
I know that some people put gravel down (being careful of the size & shape, to not hurt their feet) so that they can hose it down when they clean - but that may not be an option for you. How will you get the water out?
As it's completely water-tight, you'll have to keep an eye on any water building up if you have heavy rains / snow.
Obviously, this will dissolve any chicken poo and make a not-so-nice mess, and will lead to them getting soggy feet. You may want to put build some kind of raised area out of bricks (or something) to help them keep dry if it does get wet.
Are you considering putting a roof over the run? That'll obviously keep the rain off and will provide shade in the summer.
You'll also need to ensure that you put some grit down for them, as they haven't got dirt to dig it out of.