I think it varies from one FTO to another, but I highly doubt anyone who answers the questions "suitably" will be refused an invitation (unless they don't meet the entry requirements). It does seem bizarre that they are inviting people to selection days before the closing date. However, I'm absolutely confident that if you take your time and submit an excellent application before it closes then you'll have no problems getting to an initial selection day, even if you are the 6000th person to apply.