It really depends on the employer. A more open minded employer may recognize that people make mistakes, especially when they are young, and learn from them. They may not hold something like that against you. Other employers will not even consider you. A conviction is a conviction, case closed. My belief is to bring it up yourself in the interview stage and let them know what they will find, so you will have a chance to explain what you have done since then to make up for the error in judgment. If they find out about it on their own, they are more likely to make their own judgment about you without giving you the benefit of the doubt.
They say you get what you pay for, and this response is free, so take it for what it is worth. This is my opinion based on very limited information. My opinion should not be taken as legal advice. For true advice, we would require a confidential consultation where I would ask you questions and get your complete story. This is a public forum, so remember, nothing here is confidential. Nor am I your attorney. I do not know who you are and you have not hired me to provide any legal service. To do so would require us to meet and sign written retainer agreement. My responses are intended for general information only.
My concern is not so much with the reckless driving conviction as it is with the widely-held belief that "reckless driving" is often the charge that results when a DUI case is plea-bargained. Your best option is to be frank and open with the prospective employer if the matter comes up and be aware of the potential underlying alcohol-related concern when you discuss it. A number of law firms, like mine, offer their clients a pre-employment screening service to determine in advance of your job search or application exactly what information will be reported to a prospective employer about you.
My responses to questions on Avvo are never intended as legal advice and must not be relied upon as legal advice. I give legal advice only in the course of an attorney-client relationship. Exchange of information through Avvo's Questions forum does not establish an attorney-client relationship with me. That relationship is established only by individual consultation and execution of a written agreement for legal services.