Yes, in Auto Add Promo Items (Free Gift) extension there is an option to give a free product when a particular amount is spent. You need to choose ‘Auto add promo items for every $X spent’ action, indicate the number of free gifts in the Discount Amount field and choose ‘All SKUs below’. If you want a customer to have an opportunity to choose one out of several free products, then select 'One of the SKUs below'. Additionally, in the Discount Qty Step (Buy X) field you need to indicate the amount one should spend to trigger the promo rule.
If a customer should get only 1 free item no matter if he spends $100 or $200, specify “1” in the Maximum Qty Discount is Applied To field. Alternatively, you can use the action called ‘Auto add promo items for the whole cart’ but in this case you need to set the amount that should be spent on the Conditions tab: