A basic blood panel is unlikely to tell you much about your micronutritional status if your diet is even remotely normal and you don't have problems with absorption i.e. gastrointestinal disease. The only vitamins they might sample would be vitamins D, B5 and perhaps B12 and folate. I don't think these are even part of any basic health check at least for younger people.

However if there are gross deviations in a basic blood panel then nutrition is probably the least of your problems.

Just thoughts of an MD from Finland, I'm not much of an expert on nutrition. I don't eat extremely healthily myself and based on this literature review I don't bother supplementing anything else than vitamin D, which I consume 50 ug a day. I wouldn't be scared of multivitamins either, while relative risks might look scary, the absolute risks involved are miniscule.