Might it affect your getting some jobs? Yes, it might. Will it keep you from getting a job in the nuclear field? NO.
There are two types of men in the world, those that admit to occasionally gratifying themselves sexually and those who lie about it.
There are plenty of "holier than thou" types who will hold this event against you, most of whom are lying to themselves that they, themselves, never cheated in any way. I'm not denying that there aren't few "Snow White"s out there, who never cheated on anything, ever, but they're rarely part of the aforementioned group of "holier than thou"s. Most of us, understand that things like this occur, and are aware of the associated consequences. To be honest, if they'd hold this against you, then you probably don't want to work for them any way.
Some advice would be to broaden your job search (e.g., don't just focus on commercial power, but include DOE and other nuclear/radiological work). Be honest about it if asked (i.e., own your mistake, without shame or allowing it to define you). Work hard at any opportunities that present themselves, and it will soon be forgotten by all but the most ardent of Pharisees.
A quick sea story:
When I got to the Pig in Alameda, they immediately stuck me in RT Div. to qualify BNEQ. I spent all available time learning the systems, many of which were very similar to the systems at my NPTU [S3G]. I began hitting up the RT instructors for checkouts, but they were even less supportive than the NPTU instructors at S3G. The ones who weren't jackasses about it suggested that I wait until I get my TLD and then go down to one of the plant's CTG Flats right after in-port morning muster and catch some of the QPOs while they were waiting around to either get a work assignment or cut loose for the day. It sounded good. So I studied and waited for my TLD.
The day came when I got my TLD, so I went down to the plant and started walking down the systems that I'd studied. The next morning, I headed to the 2-Plant CTG Flats for my first CVN-65 checkout. The flats were thick with blueshirts, as I headed in, Qual card in hand, looking for a QPO. As I headed into the crowd, I asked the first fellow that I made eye contact with where I might find a QPO. At this point, a different fellow to my right yelled "Fresh NUB!," grabbed my BNEQ qual card, and quickly dissappeared into the crowd. Someone else assured me that everything was cool and started making small talk with me; what was my rate, where was I from, what prototype did I go to, how'd I like the Bay area so far, etc. Then some khaks handed out some work assignments and cut everyone else loose. The CTG Flats quickly emptied of people, and I was left there alone, without having gotten a single checkout. Plus, I'd lost my qual card [Bummer].
As I left the plant, I found my qual card near the exit ladder. Every blank had been signed off. Not just sleezed in by two or three guys, but with the interspersed signatures of more than a dozen different QPOs. I was lost. What should I do? Go report this integrity violation to the RT Div. Khak. Throw the qual card away, say that I lost it, and ask for another. I went to one of the nicer RT Instructors and asked for advice. He laughed about how I'd been majorly slimed with sleaziness - more so than he'd ever seen. He said that it was now my responsibility to ensure that I knew everything on that card. It was very much like the "With great power comes great responsibility" speech from Raimi's Spiderman. "It's your responsability to know the plant inside and out." He told me that I could skate the curve for the next couple of months or hurry up and qualify and get down to the plant. I crammed for another week and passed the BNEQ test and board. I was out of RT two weeks from the day I reported on to the ship, but I spent the next few years learning those plants.
Keep your chin up, work hard, and you'll overcome this. Always remember that it's no one's responsability but yours to ensure that you are a heavy toad. Excellence comes from within.
Good luck,
mgm