Hazard alert is issued for a change that has an immediate and detrimental effect on the subject. I don't think it per se constitutes a new forecast so an alt is not legally required. But it does imply a new forecast is coming. Once a new forecast is acquired then you must have the fuel.You could stick your head in the sand and not obtain the updated forecast and so continue. (Not what I would recommend)
Captain SNAFU, if the following was broadcast...
"All stations 'Hazard Alert', new forecast issued for Sydney indicating weather below alernate (or special alternate) minima's", which I have heard many times. Surely even though you have not yet obtained the forecast, you are aware that there is a requirement for an alternate and 'legally' that would mean that you are required to carry one?