The small pocket inverters create an overhead of around 0.25 amp over the draw of the load. Whether that is considerably more power is dependent on your battery
capacity and energy tolerance. If you operate it 24hrs/day, it will draw an additional 6Ahr out of your bank.
For us, using them to power short-time loads like our TV/DVD set makes more sense and gives us more options than finding, and paying more $$, for a lower quality 12V equivalent.
Similarly, you may find AC powered fans to be cheaper and have better performance than DC powered ones. Depending on your tolerance for power draw, you may find using a small inverter