I'm assuming you are talking about executing groovy scripts with the groovy command. This actually has more to do with the script calling java, then reading and parsing the groovy script and yes, it can take a small chunk of time to get things rolling. I'm curious why you think this is a problem though. Is it just too inefficient for the tasks you are doing? I've personally not been in a situation where the startup speed was really a problem, that is why I ask.
As to your question about OpenJDK (Java 7) being better. I have no idea. Sorry.