The answer is yes, as long as you do it once to be transported from the place of origin to your home, or if you take it on a trip. It is not recommended to do it very often since over time you will break the straw fibers. The best way to roll up a straw hat is to push the crown out from the inside of the hat and then roll it up.
Once you receive your hat or arrive at your destination, unroll it and, if necessary, use a steamer to return it to its original shape. Once the summer season is over or you simply need to store your hat for a long time, it is best to do it in a wooden box with the crown lowered.