If the property is bought with no mortgage, there is no Family Law Declaration required by the Purchaser.
If the property is bought with cash, unless there are very substantial assets, it could be viewed as deliberately seeking to reduce the assets available in the marital proceedings. Effectively seeking to usurp the Courts authority.
It would be a foolish person indeed who would seek to buy a property while going through a separation without getting agreement from the other spouse.
Every case is different, obviously, but if I was acting for the other side, I'd be saying, hold on now, let's sort it all out before you start going off buying a property.
mf