I have been training out of my garage for 8 contests. Never trained in a strongman gym before.
Access to implements is dandy, but not required. If you show up strong, you will be strong.
If you absolutely positively have to win every single contest you compete in, then hold off until you can get the implements (although, even then, events will change the day of the show, so you can never be totally prepared). However, if you just want to go out and compete, I say go for it.