I have some raised beds that I use for vegetable gardening. I don't put any fertilizers or pesticides and I grow all vegetables from seeds. Lately I have been thinking of purchasing young vegetable plants from a big box store to do winter vegetable gardening and planting them in the same raised beds. I would only plant the seedling and throw away the soil that comes with it. I realize the produce will not be organic but any other downside I am missing. Note that I am growing for personal use only and not a strict organic consumer.
Really all plants are organic (and by the way also few fertilisers and pesticides). The definition is about using product produces (by humans) with chemical synthesis.
On your garden, you know how you produce things, so you don't need any label (and strict rules).
For health, I don't think it matter so much: existing part of seedlings will be a tiny part of yield.
Anyway I would discard flowers and fruits, and possible I'll mark the leaves, so that I'll not eat the existing leaves.
Organic fertilisers and fungii affect much more the consumer health. For the first, try not to over-fertilize (manure tend to concentrate minerals and metals, and few metals are good for plant, too much could be toxic). For the fungii: I assume you don't harvest with machines, so you will see and discard bad fruits.
So it is more about ethics and personal choice.
I think you are a bit too far into the purist spectrum? All plants need additional fertilizer. A natural ecosystem is where all the plants are part of the system and over time all nutrients are actually in the plants. When those plants die they are then decomposed and the chemicals are released back into the ecosystem to be immediately taken up into the live plant material and micro/macro organisms that are part of the ecosystem.
Our gardens, plants in pots, rely on us humans to replace chemicals those plants need that were mostly stripped away during construction. Fertilizer is not pesticide. All pesticides aren't all BAD. All pesticides include herbicides. Pesticides/herbicides are BANDAIDS for problems we humans made. When we get better we know how to prevent ever using pesticides...well, almost. When we mix milk and water 1:9 and spray plants for powdery mildew...THAT IS a pesticide (fungicide). Soap and water is a pesticide. Scissors and cutting slugs in half at night is also a pesticide.
More importantly one should know the pH of the soil and what the plants we want to thrive in that soil love that pH.
I assume this is not a greenhouse/hermetically sealed environment. Raised beds are great (there isn't concrete or gravel below that soil, yes)? If these beds are garden soil over concrete or gravel...we need to talk. If you've made raised beds over concrete I hope you've used sterilized soil.
If you were trying to grow in a greenhouse we might be talking about foreign soils/plants/problems being introduced. But we are not. Do not throw the soil away. Starts you purchase are always done in sterilized potting soil. There can be problems when bringing purchased plants into the garden even an outdoor one but usually that is when we bring starts home from our friend's homes/gardens.
Do begin to imagine how you will rotate your 'crops' the next year. Do add decomposed organic matter whenever you are able, just to the top of the beds. It will be mixed for you by the organisms coming up out of the soil to eat the decomposed organic matter. They then go back into the soil profile and poop it out mixing this decomposed organic matter into the soil without you spending any calories! Be vigilant to see problems before they become a problem. In every sense gardening is organic, flexible, complex yet simple.