No, you can't do that. You'll have to follow the steps in the User's Guide under "Recovering from a disaster".
Note: it's significantly more challenging to restore from an image than it is to restore from a bootable backup. Since you seem a bit unsure, I'd really suggest spending the additional $100 to get a drive you can back up directly to. It'll save you time, will let you test your backup before you send away the Mac, etc...
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--Dave Nanian
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