Not quite that large. At the peak of its red giant phase, the sun's size will reach just about Earth's current orbit. Quite possibly the Earth will remain just slightly outside the sun due to the orbit becoming larger to compensate for the sun's decreasing mass, but the Earth's oceans will have boiled off before the sun even enters its red giant phase, because between now and then the sun will get progressively hotter over the millenia (well, technically this slow increase in average sun temperature has been going on for ages already, it's just really slow and masked by several cycles).