Should I register my script with the WGA before submitting it to a film festival?

I wrote a feature film screenplay (that I am very proud of). As I have
found some film festivals to submit the screenplay to, I was wondering
if I should register it with the WGA before submitting it. What are
the advantages and disadvantages of doing this as it applies to my
situation? Also, if I decide to make any future changes to the script,
would I run into problems (since it would already be registered)?

Thanks!