Yes 100%. We have worked hard in sourcing gluten free products that not only taste great but are Australian made. All the edible products have No Gluten/Gluten Free written on the labels (excluding naturally gluten free products such as olives, olive oil etc).
There are some manufacturers that have produced their goods where gluten is handled, and this is outlined on the packaging. If you or your recipient is unsure of a product when you have received you gift hamper, it is best to avoid it or get further information from the manufacturer.