does fruit tree absorb pesticide and fungicide from the root level and will persist inside the fruit it produce? (specifically lime and date trees)

Question

The specific situation is where there are two trees -- one lime and another date tree plant among the grass in the backyard where the grass area will get sprayed with conventional pesticide and fungicide for grass as well as the root of the trees.

I wonder in this case, will the chemicals inside the pesticide and fungicide will reside inside the trees' fruits? Even when the chemicals are not sprayed onto the fruits or leaves directly?

Thank you