No Jimmy, they can only begin trading again once the ASX consider that the market is fully informed. In this case, the company must make the announcement that they have already foreshadowed concerning a material commercial agreement with a sales channel partner.
The wording ("...is to last until the earlier of the Company releasing the announcement, or the commencement of trading...") is set by the ASX's trading rules, and simply means that they need to release that announcment today or else apply for a further extension of the trading suspension. You should see one or the other occur at some point today.
MyFiziq Limited are HQ'd in Perth, WA, and there is no public holiday there today (as there is in NSW, ACT, QLD & SA), so they should be onto it at some point today. They SHOULD have requested an extension pre-market-open, so they must think they are very close to being able to release the announcement.
The usual punishment for not meeting a deadline like this would likely be a trading suspension, however they are already suspended so they're probably not too bothered with that threat.