Yes the Ilex or whatever shrubs they were will resprout. They should be dug out getting as much of the roots as you can since with some Ilex species the large roots fairly close to the plant can sprout shoots.
You have had a truly frustrating experience which unfortunately is a tough way to learn stuff. However let me add a few suggestions for future landscape hirings. Ask for references and then call some to ask if they did what they promised and if they cleaned up their mess. Also ask for proof of insurance and then call the insurance company to verify the insurance is current. (Yes unscrupulous companies can take out a policy and then cancel it.) Only pay half up front and the rest when you are happy with the finished and cleaned up job. Good luck with your project!
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