Question: Is it possible that adding more import statements to your java code could slow down the time it takes to load your classes into the JVM?

Answer: 
Imports can have an effect on *compilation* time, but not on loading time or running time. Basically, if you import classes that you don't need (typically by using wildcard imports when explicit imports would do), then you can slow the compiler a bit.

However, even that effect is generally trivial unless you are compiling a huge system.
Don't confuse the word "import" with "class loading". The import statement does not cause any code to be loaded into memory. It's just a convenience that allows you to refer to classes using their short name instead of typing the full class name (e.g, "Connection" instead of "java.sql.Connection").