Will adding nutrient directly to the system cause nutrient lockdown?

Basically no it wont cause that. It depends on what nutrients are you using? Do you have raw salts or diluted nutrient water like GHE micro, AN etc. If you have diluted liquid stuff then those are already mixed with water and can be added straight to reservoir but if you are using raw salts then you HAVE to mix them separately to water before adding to reservoir cos otherwise those salts will mix and produce unsoluble compunds if added simultaneously. Also some nutrients (Like silica) have really high pH and it should be lowered to normal or diluted much more before adding to reservoir.