hello there. well, the general consensus is that it's not just wrong... it's VERY wrong not to do so. when you're running an ANCOVA (or any instance of the general linear model but we'll call it "regression" here), the adjustments that it does to your treatment groups are based on the regression line. by not adding the intercept, you are forcing the ANCOVA model to make the intercept 0. this implies that the expected value of your criterion variable Y is 0 when your predictor X is 0. in your case, not including the intercept would mean that people who do not have the biological marker have no cognitive functioning whatsoever (in whatever way you measuerd that). when you do not include the intercept you both gain power (just a little bit) because you don't lose a degree of freedom in estimating the intercept and, more importantly, you tamper with the slope of the regression line into forcing an effect and, hence, statistically significant findings. if you visualize it in a more abstract scenario, say for example your biological marker has absolutely no effect in cognitive functioning, so all the points of the regression line fall in a horizontal line (0 slope) at the mean of Y. if you force the intercept to go to 0, you're forcing the leftmost end of that horizontal line (which touches the vertical axis) downwards and since the point where the mean of X and the mean of Y touch works as the fulcrum of a teeter-totter, it creates a slope where there should not be any, implying that there is an effect and making your results statistically significant.

even though people sometimes say that not adding the intercept (making it 0) makes sense (like say i regress annual income on age. when you're a newborn it seems likely that you're not making any income), i would always argue that why are they including a data point that should not be there (unless their data really goes through the point (0,0)). in any case, removing the intercept in your particular model doesn't make sense both in terms of the design and the theory behind the data-collection.

sorry about that... perhaps other anlyses could help enlighten your research hypothesis?