nope...don't think so.... I think if you go for an X-ray every day - yes ....
The answer is "yes", with qualifications. Every x-ray causes tissue damage and danger. That being said the x-ray represented a quantum leap in medicine. Before the x-ray thousand of people died because a physician could not look inside and make a diagnosis. Having an x-ray taken represents a risk-benefit situation. Most times taking the x-ray to diagnose a potentially life-threatening problem outweighs the additional risk of a malignancy. There is no "safe" level of radiation. Every x-ray increases the chance of a malignancy. The problem is that hospitals, for purposes of legal liability take far more x-rays that necessary. And if a patient is transferred from one hospital to another the hospital (again for alleged legal reasons) repeats the entire test series. If you need an x-ray do not be afraid to take one, but... question every x-ray. Have them done in the x-ray room rather than on the "roll-in" portable machine (they gove higher doses and produce a less clear image because the short-wave x-rays are subject to vibratrion). If you are male or female insist on obtaining a lead shield to cover your reproductive organs, even if the x-ray is to the upper body. There is "scatter" and if they tell you the x-rays only hit where the light is they are misinformed.
No... I worked in a hospital where patients had to have multiple xrays in a week for various reasons. I don't believe you are in any danger... :-) Even Xray techs wear those badges to track their radiation exposure and they are in the room everyday for years with out issues. Just for perspective