Deploy 17 new computers by copying a disk image?

What you are wanting to do is not really designed for an OEM license. You should contact Microsoft about volume licensing:

http://www.microsoft.com/licensing/licensing-programs/licensing-programs.aspx

You can do what you propose, but you will have to prep your source computer with a "retail" or "volume license" copy of Windows 7.  You can't use the pre-installed OS as the source, and OEM media should not be used for this purpose.

If you don't have access to Windows 7 media via Technet, MSDN, or VL, then you can download and use the retail media here:

http://heidoc.net/joomla/technology-science/microsoft/14-windows-7-direct-download-links

VL media "should" be used, as that is its intended use, but retail media works.

The Windows 8 product key CANNOT be used for downgrade purposes.  It won't work (it never has).  You will  need to supply your own Windows 7 product key for activation purposes.  This does NOT have to be the permanent license, as ongoing licensing will be granted by virtue of the Windows 8 license sticker (blue), but you need to activate initially with a valid Windows 7 Pro key.

You can embed the product key in your answer file for automatic activation (assuming you have a license key with no activation limit) during deployment.

Dell can't/won't sell you a machine with no OS (technically they can and will if you go through the right channels), HOWEVER even if you did purchase them with no OS, volume licensing wouldn't do you any good.  VL is valid only for prior and properly licensed machines.  So, in one sense, VL is like purchasing a second license for each computer, but the benefit comes in them all being managed by a single/central license, without the restrictions of OEM software (imaging, transfers, etc.), and the ability to upgrade the OS as newer versions are released.  Obviously, the larger your organization, the more valuable this becomes, and this is how the large corporations do it.  Volume licensing doesn't really make sense until you hit 10-15 licenses, so it may not be the best choice for very small organizations.  But what I outlined in my original post will work for smaller organizations without VL (and would have worked in your situation - and it still can).  I would recommend becoming familiar with those Windows deployment options to save yourself some major time, money, and effort in the future. 

If you are able to complete one clean/full install of Windows 7 each day, it would take you 17 working days, or almost 4 weeks to complete all 17 workstations (assuming your pesky job doesn't get in the way and slow you down :)). 

Or, you can spend a day or two building a source PC and learning about imagex and capturing and storing images, then spend the next 3 days applying the image to each of the new PC's.  4-5 days.

Better yet, you can spend some time learning about WDS and setting it up (very easy), then the next day you simply plug all your new computers into the network, turn them on, and install the image to all of them at once (30-40 minutes = 17 PC's ready to go). 3-4 days.

So, assuming you still have 7 left, you could save yourself a day or three by creating an image to put on them.  Then, not only would you be done early, but you would have an image you could use for future systems or when systems need re-imaging after a drive failure, new users, or repurposing, etc.

Good luck!