No, you can't purchase insurance on the market place at any time. You'd have to buy it during the annual open enrollment, unless you had a qualifying event which means you could buy outside that enrollment period. I don't believe that any of that has been changed along with the removal of the individual mandate.
However, Congress has been undoing some sections of ACA, so it may destabilize the marketplaces. I'm not paying that close attention and I don't have a crystal ball, but I'm concerned about the long term stability and viability (even more than I had been). In other words - ACA marketplaces aren't guaranteed to be there if you need them.