My father keeps telling me my grandfather used to sow leeks in January, so yes you could sow now, and no, they don't need a propagator. He sowed for show, which may be the reason for the early start.
I have sown leeks in early February before, and they did grow fine, up until they bolted in late summer. I normally sow in March, and that has always worked fine for me.
The problem with sowing very early is you can end up with a load of seedlings outgrowing their trays/pots that you can't plant out because it is still too cold or the ground isn't ready.